Few problems here.
1) DarkBASIC doesn't support BSPs, just DarkBASIC Pro.
2) BSPs take ages to load. Any time you transfer to a new area, you'd have to load a new BSP, which would make things not exactly seamless. If you're talking about pre-loading all the BSPs, it's possible, but inefficient:
a) It would be faster, smaller file size, and easier to load just 1 larger BSP.
b) Any open area of a BSP where you can walk into a void causes problems. One major one is that you can see right through the walls (since you are behind them). Tons of extra polygons will be rendered (even if you can't see them because the other BSP is blocking your vision).