No. Definitely not. They'll probably characterize Kara in her New 52 style, so a couple of her and Pete would be too much angst for the universe to handle.

Honestly, Powergirl and Spidey would make a better couple than Supergirl and the web head.

@jonsmith said:

THANK YOU! Poor girl's been through so much, I think she legitimately has the right to call Batman a whiny brat.

Spidey with either Supergirl or Power Girl would be entertaining if written well and true to the characters.

It's possible but I'd prefer to see Spider-Man and Batgirl (Babs) crossover because I think that they would work a little better together because their skillset makes it so that you don't have to depower the other (which often times happen when you pair a street-level character with a cosmic-level character). Also if you wanted to explore a potential romance, I think those two would work better.