[From: firstname.lastname@example.org (Cameron L. Spitzer)]
Perhaps you don't *have* to for the board to run, but the missing RAM will cost you performance. Most "write-back" mbs cope with the missing RAM by treating all lines as dirty. You get a lot of unneccessary write cycles; you might even do better with write-through.
Your bargain-basement no-documentation no-brand mb might not have the pullup resistor on that socket, and it might run for a second, ten minutes, or ten years with that pin not driven. I think it's a pointless risk to leave the socket empty.