I've done this many times, mainly due to the benefit of freeing up the oven for cooking other items. You'll find lots of tips on the interwebs, but here are a few things to consider:
1. Size of turkey compared to volume of gas grill cooking area. The more volume you take up with bird, the less even cooking will be, so you'll have to employ some sort of rotation/flipping program.
2. Ambient air temp around grill. The colder it is outside, the more heat loss you will have through the cover, which amplifies the problem in #1.
3. Do not open the cover unless you absolutely have to due to #1 and #2. It will significantly affect your overall cooking times if you do this too much.
4. Even if you have #1, #2 and #3 handled, you aren't going to get much difference in flavor between the gas grill and your oven.
5. To address #4, I suggest using wood chips to get some smoke going. If you do, I've found that pecan and apple/cherry woods are good, whereas mesquite and hickory are a little strong for turkey.