Hi @Anonymous
OK, so Max can handle without difficulty collapsed meshes who individually have had just a (Max) UVW Map Box type applied through the export/import .fbx cycle, but Blender and C4D don't handle it correctly. To be honest, I am not sure of all the technical reasons why this is, but in my experience, you will make a relatively "bullet-proof" export .fbx by UV unwrapping with the Unwrap UVW modifier (see explanation below). This brings me to your question:
But once collapsed, I'm not actually sure how to view those UVs.
To view any objects UV's in Max , apply the Unwrap UVW modifier and open the Editor. This will display your object's UV Maps. To help you understand what you are looking at, it helps to understand that when you attach individual meshes that separately have UV's applied, Max:
1. Makes each previously separate mesh an element of the new combined mesh
2. Assigns a unique material ID for each element (assuming you accept the default settings when attaching each mesh.
3. Places the available UV map for that element in the first UV tile (U1V1).
4. Creates a mult-SubObject material and assigns it to the mesh.
So you can see the UV map for each channel in the UVW Unwrap UV editor window (see below)

The problem is that when you use the standard UVW Map set to box it will superimpose all 4 sides of the box so they are sharing the same exact texture pixels, even if their size is different. You can verify this in your case by clicking on individual polygons in your mesh and seeing them highlighted in the Unwrap UVW editor window. In the (ridiculous) example house I created above as separate first story, 2nd story and roof, I applied the UVW Map, selecting "Box" as the type for each, then collapsed the mesh. To the collapsed mesh I applied the UVW Unwrap editor.
I am not sure why Blender or C4D do not translate the Max UVW Map Box type correctly after you have collapsed the mesh, or whether it is affected by the .fbx export/import cycle but I have never had a problem with creating separate UVs for each mesh with the Unwrap UVW editor where you flatten the entire UV map giving each side Unique space on the UV tile with no overlapping UVs. I believe (but am not absolutely certain) that laying out the entire UVW Map of a mesh with no overlapping areas provides an unambiguous representation of UVs that better survives the export/import into other programs.
The Unwrap UVW modifier is more work intially, but for a very simple mesh like this, and using the "Quick Planar Map tool" you can do this in under 5 minutes once you know your way around the Unwrap UVW Modifier. The other advantage of learning this is that you have much more precise control of any details you want to add to specific areas of any mesh. And you can create a UV template (Tools>Make UV Template) and bring it into photoshop and go nuts with all of its painting and image tools, tweaking your maps to your satisfaction.
Sorry that I do not have a quick fix for you on this, but if you learn the Unwrap UVW Modifier, you will have more control and less aggravation in the long run. Especially if you plan a lot of exporting and exchange with other apps. Hope this helps. Maybe someone else here knows a quicker fix for you.