I have a FEC 120 under a gazebo that is surrounded by a privacy wall. There are pickets on top of the wall where it meets the gazebo roof. It's also completely open on one side.
The FEC is capable of generating a lot of smoke in this semi enclosed space.
If the area were completely screened in, rather than the privacy wall, I think it would trap more smoke.
With this being said, unless you were going to stay out there with the smoker all the time you were cooking, it probably would be fine. It might discolor a light painted ceiling.