It certainly is, you could for example install the stratum mining proxy (assuming that the pool you are mining for supports stratum). You would install the mining proxy on the computer with network access and then configure the miners to use the proxy instead of directly going to the pool itself.
Of course this is just one of many options. Other options include creating a reverse HTTP proxy on the computer with internet access, as the getwork protocol uses HTTP underneath. Also possible would be to tunnel a given port directly to the pool using SSH for example. But I think the mining proxy is the easiest option, and allows for legacy mining software to use the more efficient stratum protocol as an added bonus.
1Be aware that mining bitcoin with CPU and GPU is not profitable any more, unless your electricity is extremely cheap or you are additionally interested in the generated heat. – Murch – 2013-10-08T12:41:32.090
what if I have free computers that would run anyway? – scottydelta – 2013-10-08T14:58:06.700
1A computer idling uses much less power than when under full load. It depends on what hardware you will be using to mine, but I'd guess it'd be in the range of factor 1.5 (just CPU) to 3 (full load on GPU and CPU). If you don't pay the power bill that might not faze you, but with the miners' move to ASIC it might even take a while to make up the time-effort you put in. You might want to look into questions with the tag [tag:profitability] to get a better idea of what you might be getting out of it. – Murch – 2013-10-08T15:14:43.473