A screened room should be fine, I'd think.
It's when all that humid spa air is contained in a room with poor ventillation where you have possible problems. I can't remember the name of the condition, but some lung bacteria type of malady can affect spa users, but I recall it was pretty much limited to indoor spas. Also, high humidity in an enclosed room can cause structural problems. Hence the need for good venting. Screened rooms should have good air exchange so you should be okay.
Brewman
