Is a FaceTime Proxy Possible?
It's pretty difficult, if not impossible.  You see, all the communications with Apple are obviously done with secured SSL APIs.   As difficult as it is to impersonate another user to Apple, it's even more difficult to impersonate Apple to the receiving user, Apple controls the whole software stack.
Obviously a nation state attack could conceivable achieve this but this would surely go via hacking the mobile device of the receiving user.