Not sure if OBJ works, but you can import Alembics and FBX, even animated ones. Objects can be set to emitters or colliders. Right now, there's a restriction to ONE object though, which is of course very limiting.
But: I managed to export a simulated debris field with a floor as a single animated mesh in FBX-Format to Embergen; The Emission Node then allows to select which of the "sub-meshes" should emit and which not, and I could also set the floor as a collider via the collisions node. In same cases, that's enough of a workaround. It is somewhat of a hurdle though.
Nick from JangaFX said, that multiple imported objects are targeted for the 2022 roadmap.