Yes. Nothing wrong with that. I am doing that (and have been for months) right now on the machine I am typing to you.
Of course! But 5870 (ime) are some of the toughest cards out there, if not the toughest. It will mine good at 1000 core, just under clock the ram to 300. You should get about 400mhash, ime.
Just obviously don't run anything graphics intensive on the 5870 while mining, or you will probably fry a PSU.