Not recommended. The maximum actual aperture of that zoom lens without a teleconverter is already f/5.6. And as a rule autofocus systems have trouble doing their job with effective apertures smaller (or f-numbers higher) than f/5.6. With a 1.4x teleconverter, a 200mm f/5.6 lens becomes a 280mm f/8 lens; with a 2x teleconverter, the same 200mm f/5.6 lens becomes a 400mm f/11 lens! (All of those higher effective f-numbers are at wide open.) The f-stop loss will create problems with the autofocusing, and even manual focus is a challenge due to the substantially darkened viewfinder.
If you want a longer reach than 200mm (which effectively becomes 300mm on a 1.5x crop sensor), you're way better off getting a new lens such as the AF-S 70-300mm f/4.5-5.6 IF-ED VR lens.