Maybe, it depends on the specific media you have. Some Apple install media will only install on the specific hardware type specified. Others are more flexible. You can try, but you are technically violating the license terms of the software you do have.
From your Mac Mini's restore discs? I don't think so; Apple has been making those discs hardware specific for two or three generations of computers. Your G4 MacMini may have the older more open restore discs... only one way to find out!
I tried this a couple of years ago with the OSX 10.4 discs that came with a white flat screen iMac and it didn't work.