Right now, the 'Make Mesh Geom' capability is not exposed to the API -- it only available from the GUI.
Please add an Issue Report to the GitHub page to remind me to add it soon.
If you are set up to compile OpenVSP, then this change would be relatively straightforward. I could give you some tips on where to start and how to go about it.
For External geometry analysis, OpenVSP first performs the equivalent to CompGeom on each component -- if they don't overlap, then you could just run CompGeom and export the results.
If you're specifically interested in the intersection volume, that won't work.
Rob