The map from the stack to the space is a proper homeomorphism - so yes. Brian Conrad has a "modern" proof of Keel and Mori's theorem on the existence of coarse moduli spaces which you may find interesting (and can find on his webpage).
– mdelandApr 8 '11 at 12:31

mdeland: Your comment should be an answer.
– S. Carnahan♦Apr 9 '11 at 15:48