As put in my other post, it wouldn't be good, but it certainly wouldn't be bad depending on what you class as a 'computer mic'.. My friend recorded some vocals for me using some crap £6.99 ($10?) computer mic he bought from a cheap shop, and he managed to get an ok sound from it.
Unless i'm wrong in thinking what a computer mic is..
Again, what i said in the other post - if your serious, chip in a bit of cash and get a bit of gear for a sound card and a mic.