I actually came across this myself, but fortunately realized this little thing about the system speaker before buying my parts.
I was going to replace all the inside parts, including the PSU and all, and keep only my existing Micron case... and it didn't have a speaker. The old Tyan motherboard I was replacing had a buzzer built into the board. But it also had provisions to disable the on-board buzzer and hook up a system speaker if one wanted to.
During my research for boards, I found that some boards had the buzzer, but most didn't.
The Abit KN8 Ultra I ended up with did not have a buzzer. I used an old case speaker from a very old Micron that I still had in the attic (originally a P90 from '95), hooked it up to the board and just laid it at the bottom of the case. The problem I had was that the case button couldn't start the motherboard up. I got around that by stringing the two wires from the power button connector on the board out of the case and just touching the contacts momentarily to start it up. Good thing I had the speaker, because I got a constantly repeating long beep that indicated a memory problem. It turned out to be that I didn't seat the modules in all the way. After reseating the modules, it booted up just fine. I wouldn't have known of a problem without the speaker and would have wondered why the machine wasn't booting up.
I ended up buying a new case that evening (a quick run to the local CompUSA) because I wasn't about to hot-wire start my machine every time I wanted to turn it on. It was an Antec CS600 Server case that had a speaker. So most cases should have a speaker, but I guess not all of them do - even by the same manufacturer.
Not having a speaker hooked up won't hurt anything, but any post codes that may occur from problems later (or from any problems right now) just won't be heard.
It turned out that my power button problem with my old case could have been solved with an additional ground wire from the button's circuit board that it's mounted to connected back to the motherboard. But I've got the new case now, so I don't have to worry about it.
Joel