Before I had cable I was using dsl and I was getting about 1-1.5Mbps, usually, but it was sufficient for xbox live. You wont ever be able to host any games, and your connection might not be the best, but I think that you would be able to play games online.
Well 1mbps is about 125kb download speed. It might be enough but it depends on the game, graphics settings, and you need to make sure you aren't doing anything else on the network while gaming. Its cutting it really close.