Software needs to run on hardware, thus there is always some sort of computer running, which hosts your webspace/gameserver/whatever.
What do you mean by Java? It can run on both sides; client or/and server. If you manage to write a dedicated Smokin' Guns server in java and run it on your server, you could aswell just use the default executable.
Like I said before, it dependes on the hardware of the server as well as the internet connection. I may easily set up a server at home, but pings won't be good due to DSL and many hops instead of 1GBit uplink to backbone
You could, like moRtem suggested, rent a gameserver. Or if you are able to, manage a dedicated server, which can basically run any software you like.
Just do a search for Quake 3 gameservers and contact the company, whether they will also set up Smokin' Guns.