First of all, don’t listen to AI. It doesn’t know what it’s talking about. (Literally, in fact.)
And indeed, looking at its response… no, that wouldn’t work, I do believe.
Or at least, not alone, and somewhat depending on whether you want to actually enter the cave, or just look into it.
In short, a GeoMipTerrain is, to the best of my knowledge, just a heightmap: it essentially records a single height-value for each point, and generates a mesh to match those heights. As such, it doesn’t allow for things like overhangs–or caves.
Now, you could generate a hole in your terrain via a few different approaches–but that still wouldn’t get you an actual cave in there: you’d just see emptiness behind the terrain mesh.
One way or another, you would want to produce geometry for the cave interior, likely without using a GeoMipTerrain (e.g. by modelling it in a program like Blender).
(Theoretically you probably could make your cave via… I’d guess two GeomMipTerrains. But that seems likely to be finicky to get right.)
Simply put, you would alter your heightmap to account for the space occupied by the building, I believe.
Here I’d suggest taking a look at the manual page on how to control render order, as well as this thread regarding a similar question.
It’s also possible that the stencil buffer might be of use, although I don’t have much experience of that myself, and so don’t have much to offer regarding it.