It appears a bit iffy. Here's a quote from post asking about compatibililty with the 18-200 and the 80-400:
None of the current Nikon teleconverters will work with either of these lenses. The Kenko Teleplus Pro 300 series of teleconverters will work with the 80-400mm VR. The situation with the 18-200mm is a bit iffy -- at 18mm the clearances are quite close, so the teleconverters should be used with caution if at all. Kenko specifically states that it does not recommend using their TC's for lenses that have a zoom range that starts at under 50 mm.
You can find more in the Filters and Accessories section under Mastering your Nikon Lenses.
I've used the Kenko 1.4x teleconverter on the 18-200 with no problems. It seemed to autofocus OK, and image quality seemed good. I haven't put the combo to much use because I have longer lenses. I just tried it to see how it worked and it seemed useable.
On lenses I actually have used the Kenko on more (55-300 and 80-400) I have found that the lenses will autofocus without problems in good sunlight, but even in overcast daylight conditions autofocus becomes iffy. So, I'd expect the same with the 18-200.
Overall my view is that on slower lenses a teleconverter is an inexpensive way to get more reach if you need it, but not as good as having a longer lens. The 55-300 is just a bit more expensive than the Kenko teleconverter, but a much better way to get that extra reach.