No, Stella can't be the mother. And not just for the bear thing, although yes to that. (Srsly, even people who haven't seen the movie know who the characters are! They're iconic damn it!)

Stella can't be the mother because Ted isn't ready for it - he's making all the same mistakes with her that he made with Robin. Being into someone and wanting to make a commitment doesn't mean you are right for each other! I'm hoping the significance of the whole Stella story is that this is what prepares Ted to really find his OTP.