I think it'll take smoke, cooked or uncooked, and at any temperature as long as it's a bit moist to "catch" the smoke.
A lot of people believe that food stops taking on smoke at a certain temperature. It's easy to test that. Let the food get to that temperature (or above) in the kitchen oven, put it in the smoker and spritz it. See if it takes on smoke flavor.
There is a point where food stops taking on more smoke flavor. It's when the surface is dry. People that observed that no more smoke flavor was added after a certain point attributed it to the food's temperature rather than the surface condition.