You can try to shame people into not bringing up hotspots, but you cannot really stop them. There are legal limitations: http://community.arubanetworks.com/t5/Wireless-Access/The-FCC-has-clarified-their-stance-on-wireless-containment-but/m-p/226342#M46143
The best thing to do, would be to make your wifi so much better that it is a hassle for people to use hotspots.
Most hotspots use 2.4ghz band (some can be configured for 5ghz, but that is less prevalent), so that would only affect 2.4ghz clients in most circumstances. In a typical high density evironment, you would typically need to have an access point for every 30 users to make things comfortable, so 4 access points might be overkill.
- You should be operating with 20mhz channels on the 5ghz band so that you can have as many channels as possible.
- You should also enable broadcast filtering on ll your virtual APs to ensure that unneeded broadcasts do not compete with your legitimate traffic.
- You might also want to have the transmit power on the access points in that room as low as possible, so that those extra APs do not cause any interference or degradation outside of that room, or that nobody outside of that room would want to connect inside that room.
We do have a high density validated reference design guide here: http://community.arubanetworks.com/t5/Validated-Reference-Design/High-Density-Wireless-Networks-for-Auditoriums/ta-p/155578 but the bullet points above are just concerns based on what you mentioned in your post...