It's a nice idea,but I think you understood the aliens the wrong Thing's only aim is to spread its kind by imitating people,acting like them and then imitating other people,who would act like these other imitated people and then imitate other people,etc etc.
There is no way an imitated person would blow its cover by admitting it is an imitation and keep talking as nothing its cover is blew,it would just try to imitate the guy who understood he's an imitation,and the imitation has 50% of succeding,50% of failing(and if it fails,some part of the imitated body's would surely detach and become an independant being,like what happened with Norris' head).