How do I set up physics objects in C++ for a complicated actor

I’m generating an actor at runtime out of multiple meshes, and I want it to behave physically with the world (imagine like a Katamari ball). And the meshes themselves are generated at runtime, using a component similar to the GeneratedMeshComponent on the wiki at A new, community-hosted Unreal Engine Wiki - Announcements - Epic Developer Community Forums

So right now my actor looks something like this:

AMyActor
    USceneComponent
        UGeneratedMeshComponent
        UGeneratedMeshComponent
        ...

However, since the actor by default doesn’t have any objects in it, I don’t seem to have the physics settings in the editor like on the static mesh class.

What do I need to do to get physics to work on the entire actor? Am I doing this totally wrong? Should I create a custom SceneComponent just to hold the UBodySetup that manually merges all the data from the procedural geometry it holds? That seems easy to break if the components get out of sync.

Also, if I put physics data on each component, will they interact with the physics system independently or is there some system that makes the actor into a coherent whole, welding the masses from each body together?

As of 4.5 you should be able to weld bodies together using AttachTo with the weld bodies option set to true.
In this case you could have an empty scene component and start to slowly attach components (or actors) to it with that option set to true.

This sort of worked.

(1) I needed to make an empty UPrimitiveComponent instead of USceneComponent so there would be a physics object to weld onto.

(2) I needed to modify the engine to allow the UPrimitiveComponent to create its physics body even without any physics shapes, otherwise the weld would fail due to lack of a target to weld to. See https://github.com/EpicGames/UnrealEngine/pull/615