I use the Sigma for day sports, mainly youth baseball, football and soccer, rodeo.
I've had it for a couple of years now. IQ is great , HSM is fast. I do use a monopod a lot if I'm going to be holding it for a couple of hours.
It does sub as a birding/wildlife lens, with a tc, and it does handle it great. But, I see you have the 400mm 5.6. I would use that for my birding lens and the Sigma for sports .
But I see you also have the 400mm 2.8L. So with the other lens you have I wonder why you need either of these lens. If I was you, I think I would upgrade the 20D and use a 2 body set-up and not worry about buying another lens. Unless you upgrade your 70-200mm f/4 to a 2.8.