So basically, maybe.

Thanks for the different takes so far!
Special thanks to Gillbob316 for his way more in-depth take on the theory.

What I forgot to mention in the OP was that I think its also possible for some different character (such as Quan Chi) to get in Fox's head and that after his death, he would somehow be reborn as Havik. I think the idea that Havik as more of a force that inhabits different bodies is more interesting though.