*Absolutely.* (Disclaimer: I'm not diagnosed with Asperger's/ASD - just considering whether to be evaluated.)
In fact, subtly imitating characters is a (secretly) defining trait of my entire life.
In elementary to middle school, this ranged from tapping my foot - because Sonic the Hedgehog does that - to saying a sentence said by Zechs from "Gundam Wing" in a situation that had nothing to do with that show. As an adult, I smoked cigars for a bit because Sir Integra from "Hellsing" did that.
Frequently, though, my favorites are villainous, dark or misunderstood characters who nonetheless have sympathetic qualities. From a young age, I naively imitated or had imaginary conversations with some inappropriate and macabre characters, simply because I understood that they were "dark" but had yet to comprehend the gravity of the things they'd done. And even now, as an adult, I gravitate toward aberrant characters.
And strangely, while I was emotionally bound up in my small imitations, I half wanted people to know what I was doing and half wanted them not to know. My feelings regarding each of these characters were so oddly personal that it would feel both pleasurable and painful if someone recognized who I "was" at a given moment.
The bizarrely personal nature of this interest is part of the reason I didn't do much cosplay - I think that was somehow too overt, and I might've recognized that some of my characters would be ill-received. However, I'm bolder today and I might do it now.
I played a storytelling RPG online for a time, with a few friends and lots of others I didn't know from life. I became so pleasurably addicted to that game that I might stay up until 3-4 a.m. when I had to wake up for work at 6-7 a.m. During this time I got rather sick, which convinced me to stop.
I strongly suspect that this affinity for playing desirable characters - especially juxtaposed with the characters of my few close friends - led to my obsessive behavior around that game. I wish I could fit such a thing into my life more easily.