Probably a bit, and while dryer sheets apparently never go bad, the scent seems to transfer to the clothes after being used- sure it might be from rubbing against it so much, but I suspect the heat has something to do with it as well, so it could be that after a while it doesn't smell as strongly.

Can't be certain on that though. (And my brief foray into strange google searches has revealed they have a bunch of extra uses- or rather reuses like keeping your shoes from stinking to filling up purses/bags and stuff with them so they hold their shape and smell good when you eventually use em, a bonus factoid for you)

The biggest issue I'd say with your idea of putting dryer sheets on airvents- aside from they'd probably blow away, is that it'd block some of the airflow a bit, slow it down or whatever, take it a bit longer to get your house's temperature up or down, might increase the electric bill by a tiny bit, I find it quite probable that it might cost more than just putting a glade plugin in every room of your house.