Split solid into disconnected parts

[wtaisto]

Say I had a solid that represented a large box, and then subtracted from it a large skinny plane through the middle, basically cutting the large box into 2 pieces. Is there a way to detect the fact that the result actually contains 2 separate watertight entities?
I have a simple attempt at this working based on:

1. Enumerating all of the polygons in the solid
2. Build a set of graphs where each node is a polygon and each edge means a pair of polygons share a vertex
3. Detecting the number of connected graphs generated

The above approach feels a bit brute-force, and there are cases where it will fail, such as a pair of cubes whose interiors do not overlap in space but the cubes share a single corner vertex, or share a single edge without faces touching.

Is this idea of "a Solid contains multiple bounded regions" somehow available via your API directly?