As a person said before, if Valve have to shut down Steam, they will issue a patch that allows you keep playing your games.
Oh - also, if your computer isn't up to it, it could certainly cause bottlenecks in your CPU, which translate to ping issues (and other things, but ping is easily discernible more than say, buffer rewrites :P). If you're running a dual-core or lower, I'd certainly recommend not running Steam at the same time as anything else. Steam can easily chew through a chunk of processor time on slower systems. The newer version of Steam uses about 10x as much passive memory as the old version did, though it's still not much even for - say, a dualcore with 4gig RAM shouldn't notice it.
Also, in relation to a later post - you can play plenty of online games in offline mode. They just have to not be games using Steam's DRM as their online authentication. Many don't, and use traditional CD keys, or even accounts (most new EA games) for this - they'll still work online in offline mode. Only a limited number of entirely SteamWorks based games won't work in offline mode. And should Steam ever shut down - a SteamWorks DRM revocation/emulation tool will likely be released in short order. (per my previous post - they've already tested such a tool and know it works, but make no guarantees they'd release such - as it depends on what agreements they have with individual publishers - particularly those using Steam as the only DRM for their game).