Would a BSP switch sync in multiplayer. Or, in other words, do timers sync in multipayer?

what exactly are you trying to do? i bsp change does not sync but if the bsp that the player is switching to is exactly the same as the other bsp, you could do a day/night effect locally. it wouldnt sync, but it would be something

well because what I had in mind was:

The map takes you through various settings. You start out in a laboratory, where a machine breakdown sends the entire complex spiraling through space-time. The map has different stages, each a unique tileset, and has pieces of the lab integrated throughout the map, as if you are seeing the past and future of the lab. You get five minutes in each area, and at the end of each five minutes you must make your way to a 'safe zone'. This is where the current and next BSP is common (safe zones change from BSP to BSP). If it reaches five minutes and you are not at the safe zone, there is no telling whether you will spawn beneath the geometry, or die because the ground suddenly appeared far below you.