kind of, but it's not officially supported by the manufacturers...for example I've got a friend with the DFI Ultra-D nf4 board...it requires a 24pin PSU but he uses a 20pin PSU and has never had an issue with it...a lot of people seem to use a 20pin in a 24pin mobo and haven't had an issue, so you could always just try it for yourself and see....my PSU happened to come with a 20 to 24pin adapter so I use that
My 24 pin mobo bu asus takes a 20 pin connector i wasn't sure so i ordered a new 24 pin form newegg but when i recieved my parts i checked it out and my mobo took the 20 pin Psu