It could happen, but I don't think it would be very good, and that's speaking as someone who likes the marvel universe films.
The doctor is always the ultimate hero in doctor who, he may have companions or people like river or jack who help or occasionally do more to save the day than he does, but he is always cast as the ultimate saviour. As such I really can't imagine him being 'just another guy in the team'. I don't think anyone can portray a time traveling alien adventurer as being an equal to a guy with a metal suit, or a strong guy with a shield. The only person who comes close to being equal to the doctor in the avengers is thor, as they are both classed as god's in there own way, but i'd still say the doctor is better because he has time travel and thor can't exactly regenerate (and again I say this as someone who likes the marvel/the avengers, it's just that they are no equal to the doctor)
Besides, doctor who is quintessentially Brtitish at its core. It's tone and style are British, and to allow an American enterprise to take it over, it would probably lose all that makes it what it is, similar in a way to when Americans try to do their own versions of our shows and 99% of the time they fail miserably. Plus with the who universe, we've already got the embarrassing duo of he tv movie, and torchwood miracle day which both stand as a testament to why the Americans should never again be allowed to get their hands on it.