Doubtful, they are still pretty young by all accounts.
But I wouldn't be surprised if the season ended with them in a close relationship, because like you said, things have been building up for a while. Boyfriend/girlfriend sort of thing.
However, with 10 episodes to go, anything can happen. Rumor has it that Zuko's joining the gang, so it's entirely possible a spark will happen between him and Katara instead (sorry it's not you Zukofangirl2006!).
Now-- flame away.