Queens Gambit Accepted with 3.Qa4+

I dunno if i've ever seen this played before.  Clever.

White should play e3 instead of Qxc4...

true, but he's trying to refute the immediate recapture of teh gambitted pawn.

The QGA isn't a true gambit, as white can easily win it back and trying to hold it leaves white with an extremely good game. White shouldn't be playing an opening that he doesn't know anything about.

The problem with 3.Qxa4+ isn't so much that White can lose a pawn if he continues to play poorly. The problem is that it develops (and exposes) the queen way too early. 3.Nf3, 3.e4 and 3.e3 are the standard replies. All are normal developing moves, and all will lead to recapture of the pawn, with advantage to White if Black tries to hold on to it.