Can I export my finished game with BSPs?

BSP can be more of a performance hog than static meshes. You can ship a game with them however, if you convert everythign to static mesh you will need to fix the Lightmap UVs (easy enough in the static mesh editor), add collision to all your static meshes, and essentially just do a pass on checking to make sure everything is working the way you want when you convert them.

When you convert the BSP to static mesh don’t select them all and make them a single static mesh. This is a bad idea.

There is two things on the wiki lighting guide that can help initially:

Ultimately, you can package games with BSP, not always recommended, but it’s possible.