Some details seem to be missing.
You have OS X Server? Which version? 10.5, 10.4? "OS X Server" isn't very specific, but I can assume it is order since you mention 10.6 Server.
Can you still use OS X Server? Which version do you want to put on the Mac Mini? If you want to put 10.5 and under, then yes you can. 10.6 cannot be installed on a PPC Mac.
Will it update? Depends on what version the install DVD. If it is say, 10.5.3 it will update to 10.5.8. There will be no more point updates after that, but it will get security updates.