I'll go along with Squishy's analysis. I use mine for wildlife, including BIF, and also motorsports and running dogs. I get by quite well with the 100-400 for sports such as motor racing, where subject movement is usually very predictable and easily tracked, and the IS can really help with the slow speed pans, but I think football might be another story.
I've never actually tried shooting football, but where you have a high degree of random action the IS will not help and you'll need high shutter speeds to freeze subject motion, which should also take care of camera shake for you, more so if you use a monopod. The bigger issue would be achieving those high shutter speeds in less than stellar light. Of course the 400L would have no advantage there either, and without the zoom may even be too long at times, especially on a crop body. But I think where players are changing direction and speed at random any advantage in the AF response is likely to be a big plus. I think something faster than f/5.6 would be very useful, not only for shutter speeds, but also AF performance and subject separation.
What about a 70-200/2.8L IS II and a 1.4x and/or 2X TC? That will give give you a more versatile setup and the new 70-200 is supposedly mad sharp. Another option, if you have deep pockets, would be a 300/2.8 and a TC or two.
The 100-400 is a great lens, and I love mine, but for football....... I'm not sure. Think winter, rain, dull days and so on. As for sharpness, here is a sample from today while out walking the dog. It's just a practice shot of a DIF. Here is a 100% crop of a shot wide open at 400mm before and after sharpening. You can see how small the bird was in the frame. I also don't think 1/1000 was sufficient for a perfectly sharp hand held shot at 400mm on a 7D viewed at 100%, but you do what you can.
Here are a couple of shots from today of the wee doggy having some fun. All are wide open at 400mm. No edits on these except WB....
There are more examples from my 100-400 in this thread -
http://www.talkphotography.co.uk/forums/showthread.php?t=289585.