I don't know about throwing it on the grill. It won't hurt , of course. I do beer can chicken all the time and usually have my temp between 250 - 275. I'm not familiar with your smoker. Smoke and Spice cook book has a nice recipe I've used a few times. Their jalapeno/peach BBQ sauce is really good on chicken. It usually takes 4 - 5 hours to smoke a whole chicken, course, I usually smoke 4 to 6 at a time. If I grill it then I grill it split like was mentioned above and I put a heavy brick (wrapped in foil) on top to keep it even. If I smoke then I smoke it and don't bother with the grill.