Hi Ian,
I have that set-up sitting on my couch right now.
To answer your question honestly means that I can only talk from my own experiences with this combination.
The D7200 is a fantastic little camera with 24Mp sensor and around 8 frames per second, it also has 2 SD UHS II card slots and it writes the info to these cards with impressive speed. RAW buffer is about 12-15 shots, depending on file size and card speed. Jpegs you can just keep banging away. For BIF, the AF system is not quite up to the standard of the D500 but certainly acceptable and also note the buffer capacity.
This body is fully customizable and indeed has tow 'My Menu' options to set it up how you like, maybe one for stationary birds and one for BIF, but it requires the turning of a wheel on top of the camera.
The 200-500mm zoom is supposed to be F5.6 and it is certainly stamped that way, however, my example seems to be at least a half stop darker than a Prime F5.6 and this might have something to do with the extra glass in the zoom, maybe I don't know? It is certainly a heavy lens but a lot lighter than a prime of the same size, discounting the PF version due to cost. Out of the box, you will receive a beautifully made and functioning lens with a zoom range ideal for birds. I set mine at 500mm and thought that it was a cheap buy for a 500mm lens but then found out that 500mm was too much on occasions and the zoom has come in very handy on many occasions. You cannot rely on the lens being 'spot on' straight out of the box and indeed my example requires a setting of +5 on the AF Fine Tune. The only niggle with the lens is the lens hood and unless you add a little bit of gaffer tape to help secure it, you can guarantee on sending Nikon $80-90 for a replacement !!!
As a combination, I cannot think of a better 'budget' set-up and if you check the Nikon Forum on Fred Miranda there are hundreds of very happy users continually posting images from this exact set-up.
I think that anyone who uses this set-up will find it necessary to be cautious about wandering into high ISO territory as noise can be a problem but it is a problem for all cameras and careful choice of settings plus some noise reduction in post processing shows great results.
I use this system as my 'back-up' gear and quite often l will grab it and take it out when I can't be bothered carrying the 'big' gear around.
I hope that this helps Ian and anyone else considering getting hold of this camera and lens. For under $3000 it is serious equipment at a great price. . .
Cheers,
Bruce