In one of my missions a (minor) canon character was narrating, and we used a crash dummy just like for any other mission. We exorcised it, and it turned back into a rubber cube. Pretty straightforward.

As for mimicry, I'd say that're more or less the case - in a first person fic, there is no physical manifestation of the character in question because it's supposed to be the reader, so the dummy gives it that physical anchor instead of letting the agents be forced into it. I'm not sure what would happen with a POV change, but it could probably be as simple as the dummy's plastic skin turning into proper flesh for a minute, and then flipping back.

...Was that any help? I feel like I've missed your actual question and explained what you already know.