How do I run Steam from behind a proxy server?
Of course you could run Steam behind a proxy server, provided that the administrator opens the necessary ports.
You can find a good guide directly on Steam Support: Required Ports for Steam.
Basically in order to just run steam you need:
* TCP 27014 to 27050 inclusive (Steam downloads) * UDP 4380
Steamworks P2P Networking and Steam Voice Chat
* UDP 3478 (Outbound) * UDP 4379 (Outbound) * UDP 4380 (Outbound)
Than it really depends on which multiplayer game you want to play. In this case additional ports opening is required.
Instead, if you want to play only single player games, the steps before should work in 95% of games except those that requires additional connection requirements, like, for example, some Ubisoft games, some Game For Windows Live (GTA IV), etc.