Bad idea, if I mine my computer is very slow, I have to stop my other programs.
If you mine with poclbm or GUIminer try using the -f "frames" switch and a high number. Something like -f100 or -f200 on each of your GPU workers should free up enough cycles to let you use the computer like you're not even mining at all. Just keep trying a higher number until you get the effect you want. The higher you go, the lower mH you'll get though. So it's a trade off. I think there is a similar switch for Phoenix but don't remember it.