Can but not necessarially will. After all, demons do want you to sell your soul to hell. So, if a demon is [strike]over[/strike]confident and wants to tempt you into some sort of pact, it might not hide its nature. On the other hand, many demons are cowards.
Yes, this is perfectly viable.
The covenant's Aegis should keep out minor demons anyway. And those that sneak in by possessing somebody will be affected by the Aegis if they try to use powers etc within the covenant.
Unfortunately, there are still problems with slinging DEO spells at all and sundry on the off chance that the target is a demon.
When you cast a spell at a target that target has no idea what your intentions are (unless they've been using InMe to read your mind, in which case you have bigger problems!).
If you cast at another Hermetic magus all he is going to see (at best) is that a stranger is in the process of launching a PeVi attack against him. That is exactly the sort of action for which you will recieve in return a Fast Cast Pilum of Flame (or much worse). Will most magi (who are capable of replying) wait to see whether your PeVi attack is a DEO or something that destroy's their Parma Magica?
Magic critters, faeries, etc will also, if they recognise that you are casting a spell at them, consider this at best rude, at worst an attack (esp. if they recognise that it is a PeVi effect). Even mundanes who you mistakenly target with this will be offended, afterall if a mundane sees you casting spells at him then the social effects of the Gift will have him interpret your actions in the worst possible light.
So, while PeVi is a viable way to detect demons, it can create problems for you depending on the context.
It also isn't fool-proof anyway. If the demon is big enough to survive the first strike, and recognises what you are doing, it might create an undetectable illusion that it was unaffected.