I love this. I can imagine River and Ripley would be teaming up to kill it, where as the Doctor would just be fascinated with studying it. Then running away when it tries to kill him. After that, he probably would be more inclined to go along with River and Ripley.
I could see a Doctor like Eleven being more fascinated with studying the Alien, same goes for One or Four. A more active Doctor like Three would recognize it for the threat it is and make tracks to destroy it, while Two would do the sensible thing and run.
Why do I get the feeling the Alien will end up being afraid of him at the end? Because as that Movie defense force guy said, the Alien is a force of nature and you are going to lose, and the Xenomorph in this case is not that Force.