Pound the chicken so it is a uniform thickness all over so you can use the GF. You can marinate the chicken in the BBQ sauce. When you cook it on the GF, wipe it dry first so it will brown. When the chicken is almost done, brush a light coating of bbq sauce on the chicken and finish cooking.
If your GF can handle the thickness of the finished wrap, go for it.
"If you want to make an apple pie from scratch, you must first create the universe." -Carl Sagan