PhotoConceptsDT, I like the blue jay!
Don gives some good advice.
I've taken plenty of great bird pictures with my 70-200 (it's not even an IS...a feature seldom used for birding), even on the full frame body. Not every bird shot needs to fill the frame with the bird. Think about how to portray it interacting with its environment. And I doubt you would be capturing any small birds in flight with a 600mm lens, especially within the even narrower field of view of a crop body. They are so fast it's difficult to follow them, even at 400mm, hand held...or at least it is for me. The 600mm is for stationary small birds, or else larger birds in flight at greater distance.
I've taken some interesting bird in flight pictures with just an 85mm f/1.4 lens, in very dim light. Of course I was within 15 to 30 feet of the bird.
One of my favorite shots lately, that I have yet to tweak on, was a flock of robins, shot from hundreds of feet distance, with the 70-200. They were all on the ground in relatively low grass, which still had brown patches because it was very early spring. The brown patches added some depth and texture, though. I was also enjoying the fact that a ways behind them, was a group of wild turkeys...so I was able to take it all in, zoomed to around 200mm, on a full frame camera. Then all the robins suddenly took flight at once, so they make a line of flying small birds, in front of the group of turkeys, in one of the shots. There might have been an interesting shot in there with a 600mm lens, but it would have cut out most of the turkeys and robins, only zeroing in on maybe 6 robins and 1 or 2 of the turkeys. Even if that shot turned out great...it would not be $10,000 "greater"...