Yes it is. So long as you are outdoors and there is sun Otherwise, if you are in a dome with limited overhead lighting, you may find you need to increase the ISO to freeze the action, and in that case you might find a lot of noise.
Or, go for the 2.8 or better.
+1 - if you're indoors, f/2.8 is often marginal to get 1/1000s, and I'd nix the 7D idea, too.
On the side I am saving up for a Canon 7D.
Why? Hopefully only as a backup to your 5DIII. The only reason I can see to choose a 7D over a 5DIII is if the latter is broken.
+1 on this, too. Even with DxO PRIME, at ISO 3200+, which you'll need a lot for sports, even outdoors if the light is low, you'll be very disappointed with the 7D compared to the 5DIII.
Unless you really need the reach, I'd consider the 70-200 f/2.8L (or if budget allows - IS II) + 1.4x extender (when needed). That combination rocks for sports photography inside or out and having zoom is very handy for most sport shooting.