Someone will correct me if I'm wrong, but I don't think C4 supports point-level animation (except for its own internal variations thereof), so any cloth simulation made externally would not do anything useful once imported to the engine.
If I'm right, then you would have to animate your clothes with joints instead, perhaps by coming up with some clever method of converting a cloth sim to joint. I imagine it would be sort of possible in Cinema, by first making the cloth sim as usual, then creating a skeleton with joints constrained to multiple, well-chosen points of the simulated cloth, then bake the resulting movement of those joints and bind the mesh to them.
Tricky, and an interesting conundrum...
If I'm wrong, however, it should be easier :)