than some here seem to think. I refer you to the PPC Agents who had to permanently change into Elves, because a time distortion meant humans would have instantly died of old age.

I think the change is pretty complete.
One of my future plans kind of depends very, very much on this, so the fact that hS has already given the Jay and Acacia example helps a great deal.

I think a disguise generator generates a disguise, i.e. just the physical appearance of the agent changes. The agents do not become the species that they look like (unless they already are that species). Actually, a female agent disguising as a male of the same species will still not be able to find out what the big deal is about peeing standing up.

I like that limitation of the device. If the device could give the agent any power they'd like from the fandom they were in, the device might better be renamed the Mary Sue generator. As that is what Sues do: they take on the powers of the fandom they like, and then some.

Which is not to say that agents have not taken over some of the minor powers of their species of disguise. I once disguised my agents as fairies from Torchwood, wings included, with which they managed to fly. That is if your definition of flying is falling down and occasionally missing the ground. (so they got the power, but couldn't control it. Ah, conflict)

Anyway, I guess if an agent disguised as a shapeshifter they'd probably be changing appearance throughout the story. And knowing how PPC equipment works, they'd be changing appearance at random, and quite often at inconvenient times.
Would that work for your story?