I used my Mac Pro (early '08 model) in a small college dorm room for a while, and never had any serious bleed issues with it. Sometimes I put a chair with a blanket draped over it between the Mac and the mic, but that was about it. I wouldn't be too worried about it.
Of bigger concern would probably be any external hard drives you might have. I get a lot more noise from them than my Mac, but they still don't get into my audio much with the above mentioned method. Of course, if you have externals that aren't being used during tracking you can just turn them off--this is what I do with my Time Machine drive.