A:Answer If you're wondering whether or not it will fall down, I'd say it most likely wouldn't even with strong wind. Especially if you're going straight into the wood of the gazebo, and perhaps use a slightly larger screw than the provided ones.
I couldn't speak to how well it would keep dust/sand/dirt out of the motor, not to mention any bugs that find their way in there. You might be able to put some kind of wrap around the housing to ensure it's protected.
It's a great screen, so if you can make it work I'd recommend it.