There is a potential for greater overall bandwidth usage. If a user reaches the traffic quota for his/her assigned IP address, the user can immediately connect to another user's IP address via wireless without waiting. Using this method, users can hop among available IPs resulting in overall increased traffic.
If wireless is banned, there will always be a large percentage of IP addresses that never reach the traffic quota (i.e. the "high bandwidth users" will never have access to the "low bandwidth user" IP addresses).
If that traffic increase is enough to crash the institution's network, then their network infrastructure isn't designed to handle the load and should be upgraded.