I recently uninstalled and reinstalled the game to play SoA with my friend (Who does not have ToB). I installed the latest of the SoA patches. Now that I am done playing with him, can I merely install ToB and then the latest patch on top of that, or will doing so screw up the game?

If and only if you have SoA, Official patch and no unofficial content (even the SoA baldurdash might cause troubles, although I doubt it) you can install ToB safely.

If you have any actual mods installed you will have to remove them. weiDU mods should be ok. Old style mods, best bet is to start from scratch.