I use the 70-200 4 for a lot of wild life photography. I would agree that for birding it would be better to get at least a 300mm but budget can be an issue. You can look into getting a doubler but then the amount of image quality loss and loss of -stop can make that decision null and void.
This shot was taken with the 70-200 4 and then cropped almost 200% and I think the sharpness hold beautifully, which is the main reason I chose the 4 over the 2.8. It may be great having the extra stops in low light but in practice try getting good focus on a moving object at 2.8 with a 200mm or longer lens I dare you (Especially birds).
http://www.flickr.com/photos/jon-luke/4711629662/in/photostream/
This shot was taken with the 70-200 4 and then cropped almost 200% and I think the sharpness hold beautifully, which is the main reason I chose the 4 over the 2.8. It may be great having the extra stops in low light but in practice try getting good focus on a moving object at 2.8 with a 200mm or longer lens I dare you (Especially birds).
http://www.flickr.com/photos/jon-luke/4711629662/in/photostream/