Get used to NEVER getting a straight answer on this forum, unless I read your post.
Can I just use one of my 5770's as the output to my monitor and continue mining with my 5870 with a clock of 1000+?
Yes. Nothing wrong with that. I am doing that (and have been for months) right now on the machine I am typing to you.
Will this degrade my 5870?
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.