Busting the Winawer French

Hi folks, 

At my club some people play the Winawer and expect white to play 4.e5. Then they use a whole library of theory. So I was thinking... 

What about 4.a3? It forces the bishop to trade on c3. Of course black can then take on e4, but after Qg4 white wins back the pawn. The theory as far as available says it's still equal or a little better for white. So what do you think?