It is possible. I've been to hotels that have pulled nonsense like that before. The usual ways they do it are:
- Blocking specific outgoing ports used by your VPN (by far the most common way)
- If they provide DNS via DHCP, they can block requests to your VPN's hostnames
- Detect and prevent packets with security handshakes - which would essentially stop you from have a secure connection anywhere.
Why they do it, I dunno. But it is technically possible.