Yes. So, it comes down to what foci the troupe says are allowable.
It is difficult to see why a focus, say, in "archaic Roman armour" wouldn't apply both when you are casting spells that target "archaic Roman armour" and when you are enchanting "archaic Roman armour" as an item. In fact, if I had a character with this focus I would be pretty annoyed if I couldn't use the focus to enchant some Roman armour with item effects.
Sure, if your focus is "wooden wands" it is much more practical and effective than some other possible foci --- but not all foci need to be equal, and not all foci need to be allowed by the troupe. Certainly, I think that I would argue that "wooden wands" is a Major Focus, whereas "archaic Roman armour" might be a Minor Focus. I could also see an arguement for the troupe stating that "wooden wands" is not allowable as a focus. However, if your troupe allows "wooden wands" as a focus, it is quite clear what having a focus actually does.