Hi, I,ve used my 600 f4 with my D4 & D800e for shooting Red Kites in flight and have some great shots. The pro I was with recommended shooting wide open with the long lenses, worked for me.
Please forgive me stating the obvious, but I'd say a solid tripod (i.e. big Gitzo or similar) and gimbal head is a must if you want to track birds in flight. I think good technique is well rewarded with this lens, e.g. get focus spot on as there is no room for error. I found 9-point continuous with full matrix metering worked well for me - shooting against a dull/cloudy sky, and +1 or +2 stops when looking up. I've never used VR, preferring to rely on a shutter speed of 1/1500-1/2000 sec.
I started with wading birds when I first got the lens. This gave lots of chances to practise - focus still critical, but the bird was relatively stationary. Again, no VR preferring to rely on pushing shutter speed up.
I've not used a teleconverter with my 600 but found the x2 works well with my 400 f2.8 stopped down to f8 as anything less the results are too soft for my liking. Also, shooting with the 800e in DX worked well for me too for the wading birds assuming they fit the smaller DX frame.
As for carrying - it's very heavy. Add the tripod and you need a truck! I have carried the whole lot on a bike, but it wasn't much fun. However, get set up and start shooting and the hard work was well worth it. I hope you have fun and get some great results.