There are some heroics you could do with 5-shaman, and some parts of other that you could do, but it's doubtful you will be able to do them all without a tank. A shaman can't tank heroic mobs, so it would require some clever approaches to fighting, most notably, kiting.

Here's a guy who did a few that might give you some hope: http://home.comcast.net/~xbx/xbox.htm. He cleared SP iirc.

It's difficult to say exactly what you will and will not be able to do with that computer, why not just try it? I have a core-2 duo with 2G of RAM, and was surprised to find out that I actually could run 5 clients on it (and this is with a 30" monitor too, putting extra strain on the graphics sub-system) just fine as long as I didn't go into a major city or anywhere else with a lot of other players. I didn't think I would be able to, so I'd say give it a try. You might be surprised.

BTW, a big hint about that is to set the background wow processes to have a maxfps of around 15 or so. This will give the foreground process (which is the one you really care about) more space to run. This helped me out a ton.