Hi Doc,
There are enough erroneous assumptions in that to get you accused of malpractice but I am coming to your defence.
First, you don't want to barbecue a turkey, but roast it
.
Second, you can't barbecue on a gas grill.
Third, a gas grill is not a barbecue.
Click into "According to Smoky" from the opening page at www.barbecuen.com and read the "Glossary" to get your facts straight. Then read the three turkey articles. Then back to the front page for "Turkey Facts" for times and temperatures and other useful info.
If you want some smoke flavor, wrap some wood chips in heavy duty foil, pierce several small holes and put it on the lit burner.
I do not recommend stuffing the turkey, unless you have heated the stuffing to at least 160 degrees before putting it into the turkey. Cold stuffing creates more opportunity for a pocket or two not to reach 160° degrees, thereby exposing you and yours to salmonella or other beasties. It is okay to stuff loosely with a quartered apple and onion and a stalk or two of celery.
Covering the turkey would change the texture and it would be boiled bird instead of roasted. You may need to cover loosely with foil if the breast begins browning too much. And be sure to put the bird on a rack so that the bottom doesn't boil in the juices.
Have fun,
Smoky