Beyond the general like, “lol who are you”, I don’t think she’d be a good companion (for Ten at any rate) because I don’t think emotionally she’d provide what Ten needed. Ten always needed someone to say “jesus, Doctor, what are you doing, get down from there before you get us all killed” — Christina seemed way more like the kind of companion who would egg him on into disaster. Like, I don’t think Christina would ever be ~someone to stop him~. She lacked that bit of sensibility and compassion that Ten needed the people around him to have. When they find out that entire planet has been eaten by stingrays her reaction is “ew it’s in my hair”.
There might be some other Doctors she’d’ve been fun with, but I think with Ten in particular it would have been a disastuh long-term, especially reckless, barely-holding-on post-JE Ten. She has useful technical skills sure, but in a long-term situation I don’t think they’d be a good partnership.