Yes! It's an easy way to cook, and the meat will be juicy and tender, and nicely browned on the outside. I've rotis'd our Thanksgiving turkey for years now! Chicken is a snap, and fatty birds like duck are fabulous. A nice roast is almost set it and forget it.
There are baskets that you can fit on the skewer, that will hold small parts like chicken thighs to really get the fat out. I once spatchcocked a chicken, put it in a flat basket on the skewer - it was browned inside and out.
A rotis bastes the meat in its own juices and the excess fat drips out without flareups because its an indirect method. I have a rotis for both my charcol and gas grills. and use them all the time.
Get the Weber rotisserie for you genesis, a friend at work spent the extra bucks and he loves it!