Will it? Wouldn't the auditory species upon which Eyes of the Bat depends be destroyed if there is a PeIm spell destroying sound on the target?
For the sake of game balance, I would say no. Discerning is different for detecting, and it implies that there is something to discern rather than a void to fill. The discussion makes it clear that it is not the only interpretation, but then again, we are not very likely to build a consistent system of physics based on species, so I would rather rely on game balance, which has to be a troupe judgement.
If you want to allow a blanket sollution, I think it has to be The Discerning Eye. Intellego can detect what's there. InIm detects images, and if the images are destroyed, there is nothing to detect. However, spells can be made to detect any, but not every, kind of invisible things; you can detect invisible people with Corpus, invisible animals with Animàl, and the cleverest idea was already proposed, you can detect the invisibility effect with Vim.
First, we're talking about invisibility, so lack of visual species. Second, these species are coming from the air, not the being. So even if this were silence rather than invisibility, the being emitting no auditory species would be irrelevant. The reason I said "if they're solid" (liquid would work, too, but I was thinking non-spiritual mostly) is that this spell detects the boundaries of the air, so if they're spiritual then there won't be a boundary with the air.
Even though The Discerning Eye specifically works through extromission? That is stated in the spell's description -- a magical sense that works using species projected by the caster and which is reflected by surrounding objects. It is then compared to what is seen from natural species. So if the magical species is either blocked by magic resistance, or because it is destroyed by the invisibility effect (which is not necessarily the case), then the caster would detect a void at that location. The shape should be discernable, though not the details.
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It could also be that the extramission species go through the invisible object and naturally reach the wall behind. The spell description is pretty clear when there is a false image, but completely silent when there are no illusion "generator" to detect.
Second sight explicitely mentions invisibility, and I don't believe a simple spell should completely shunt a Virtue. Even abusing MR to disable invisibility for all low-Might creature is excessive. So there are reasons to limit the scope of The Discerning Eye.
For invisibility to work, the effect has to allow the species of other images to either pass through, or flow around, the target of the spell. This may be a side effect of PeIm effects, as an Image may be required to interrupt the path of species in the first place. It might help explain transparent things like water/air/glass which have little to no image of their own, so random species flow right through them.
It's possible that solid opaque objects don't actually block species either, but instead overwhelm the image behind them with their own species. So when an image is destroyed, the image behind them is no longer overwhelmed, and can be seen.
I'd agree that a single spell shouldn't replace a virtue, but Second Sight allows much more than see invisible things. It also allows one to see ghosts and other spirits, as well as allow the perception of regio boundaries.
Spells should, IMHO, be able to duplicate some aspects of a virtue. Particularly one so well known as Second Sight. We already see this with InVi, which can reveal regio boundaries. Hermetic magic can also detect and reveal ghosts. Why not invisible things and creatures? After all, a simple fog with a lowly CrAu spell would reveal them, so why not InIm?
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I agree with covering some aspect is reasonable, as the MR trick of TDE implies the one above. And if the word invisible appeared in the spell description, we wouldn't have this discussion. But as it stands there are no necessity to make that spell more powerful than spelled out. You can see why I'm not hot about turning it into a Ginsu knife that can cut anything.
What makes no sense is using optical species to detect non-existent optical species. Any other method could be fine.
It does (HoH:TL p.72):
When cast without Penetration the caster is able to spot areas of Magic Resistance (which would include an invisible magus).
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That would overrule HoH:S p.61:
Iconic species are carried in light, and are interpreted by the eye.
Hence opaque objects - blocking light and casting shadows - block the iconic species carried by that light as well.
Overruling HoH:S here might be a house rule for some troupes, simplifying Invisibility for them but sacrificing some 13th century optics.
So, invisible, but only with MR. Not that same thing.
For the other kinds of invisibility we have in TDE:
You can tell whether an image has been created or altered by magic, seeing both the original and false images in case of alterations.
So no need of singling out invisibility there - unless you use some troupe specific rules. 
That's one interpretation. Another plausible interpretation is "invisible, even with MR". I don't see why the spell would work better against something that has MR than against something with no MR.
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"created" -> Creo
"altered" -> Muto, Rego
Sorry, this quote hasn't covered removed/destroyed.
The issue Tugdual is pointing out is that the magical species will be blocked by something with MR, regardless of whether the non-magical species type would be blocked (meaning the same result for invisible v. visible). Thus it does not follow logically that this implies the same species would be stopped by something invisible without MR. That invisibility comment in the spell says absolutely nothing about invisible things without MR.
If the emitted species are optical species and the thing is invisible via PeIm making it not able to interact with optical species, in the absence of magic resistance those optical species should travel right through it as though it's not there. But are the emitted species really optical species or just interpreted by the eyes as though they are optical species. With sense-Target spells like this, it really needs to be the latter. Why? Because otherwise you grant the ability to see these things to other people even though the InIm effect isn't given to them. It would also mean, in cases like this, that the magus should look like Marvel's Cyclops without his visor. And if these emitted species are not optical species, is there any reason PeIm making the thing not interact with optical species would stop it from interacting with these other species?
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Invisibility its a Perdo effect. Anybody saying that we should be able to detect an illusion generated or modified, should remember first that we are talking about Perdo. Perdo doesn't generate nor modify, Perdo destroys (or avoids to generate in first place, choose whatever you prefer).
We aren't talking about an altered or created image, but a destroyed one. There is no image to detect. It's not a Muto, Creo or Rego effect, its a Perdo one.
It's like somebody casts a PeCo into a corpse to turn it into dust, and you insist in that you can cast Whispers Through the Black Gate into it because part of the dust is of meat origin and its not a pure skeleton.
Also, species are a natural thing, and they are not stoppable with MR (much less the lack of them, ofc).
And the species of other items around the invisible thing, MUST be able to go through the invisible thing (doesn't matter your interpretation of species or the way they transmit) or then there is no invisibility at all in ArM5.
On the other hand, yes, the invisible thing still drop shadow. And remember, the shadow to the ground its not the only one, also project shadow to the very own invisible object, so it should perceive like a bubbly thing into the air (making it possible to detect at night too, as its in rules).
Then how is someone with Second Sight able to detect the invisible, then? And why would Hermetic magic be unable to replicate that part of the ability?
Because its a Virtue, not an Intellego effect. Hermetic magic its also unable to replicate a lot of things from supernatural sources... like from the Faerie realm 
With spells, in ArM there is no a True Seeing like in D&D, thats why Second Sight exists and that why its so costly (in time) to level up.
We know, that a working VoI needs to somehow move or recreate iconic species from behind an invisible grog. "Altered" is a very general participle covering that as well as reduction of species.
This is where I said above we will run into a lot of trouble. Second Sight can see the visible species given off by things not giving off visible species? Several Virtues will let you see the visible species given off by things in total darkness?
You assume this must be the case, but your assumption is faulty. As I've pointed out and people seem to have ignored:
Just because you ignore that the visible species might pass right through the invisible thing unhindered does not mean that cannot be the case since it is possible they might go right through it. Yes, it gets really strange with modern conceptions of light v. images, but we also see this with Second Sight and with all the seeing in darkness Virtues.
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The Discerning Eye specifically does not use visual (iconic) species to detect the discrepency between the original and flase images (emphasis mine):
The enhanced sense works by extromission (sending magical species from the eyes). If these encounter any Magic Resistance, they may be blocked. Therefore an area protected by Magic Resistance will appear dark to the magical aspect of the caster’s vision.
Arguably those magical species are something different than the iconic species described in HoH_S p.61 (otherwise they wouldn't be mentioned).
But even if they were iconic species (magical one), then someting like Veil of Invisibility would just prevent them from being reflected back -- just like magic resistance.