why not?
pretty much this whole set:
British Wildlife Centre 3 1000 - a set on Flickr
was shot with flash on fill (it was a cloudy day so it was that or horrid high ISO). With something like a lumiquest softbox the lighting works well.
Also (I hate to say it) but the 80-200mm will be way too short for small birds unless you are intending to use hides and feeding stations to get them really close! (under 10feet)
If birds is your main intent bird photography starts at 400mm and a 400mm prime lens (or a 300mm f4 with 1.4 teleconverter) would be the best starting point for that sort of photography.
I have used a 70-200mm f2.8 IS lens for birds with a 2*teleconverter (with flash support - not essential but the combo needs very good lighting and I was in not so good lighting for the combo - f8 was where I was shooting to keep the sharpness as much as possible)
examples with 100% crops:
little birds photos test - a set on Flickr
An 80-200mm with a 1.4 TC is a great zoo lens - but just does not have it for true wildlifing (at least its not an easy lens to use for it).