That's a great way to do it if you can ensure adequate airflow and clean air. Also putting a projector outside the room and shining it through a hole into the room is awesome. It's like a movie theater. But, most setups don't allow this.
A projector can usually be flush mounted against a ceiling mount bracket, typically upside down. I have not seen a projector that wasn't designed to sit on feet on a table, which means that no projector vents down, into the table, or when ceiling mounted, upside down, into a ceiling. Most vent front to back, front to front, or side to side.
Noise is only an issue with some projectors. Others run very quiet and only will be heard when there is total silence during a movie.