Every time I've had it its been open top cooking over open pits. There is so much veg oil in the baste that I think you would have a smokey(and not in a good way, the black soot kind of way), greasy, fiery mess on your hands. I would opt for the weber with no lid, I think the appeal to this style is the baste dripping on the coals and seasoning the birds via smoke and steam. Just my $.02.
Life is to short for green tea and tofu; pass me another half rack and a beerů