I have heard that monsters only spawn within a fixed radius of the player in single-player mode. Is it different in SMP, or is it that because there are no players that no monsters can spawn?
As far as I know it works the same in SMP. You can find the algorithm at Minecraft Wiki. Basically they don't spawn closer than 24 blocks, or farther away than an 272 x 272 area from a player. So no player = no spawns.
You can test this yourself by joining a server that has been empty for a while (I'm not sure how long it takes for mobs to despawn) and you'll notice that it always takes a few moments before any kind of mob shows up.