Ceiling fans are not the same as whole-house fans, nor are they designed to 'introduce' any air into the room, they merely circulate it.
A whole-house fan is entirely different from a ceiling fan. A whole-house fan pulls air from the house and exhausts it out through the roof. Cool air comes in through open windows.
Typically they're installed in an attic, but some simple searching finds units that can be mounted in a vaulted ceiling with no attic space.
So yes, you can install a whole house fan.
By contrast, a ceiling fan is usually installed in high vaulted ceilings to circulate air. Heat rises, so you can get a very big thermal difference between the air the ceiling and floor. It's actually most beneficial in the winter, running in reverse, to push the warm air down out against the walls and down into the room.