Yes, jME3 can run headless. Easiest solution is letting the server handle everything and just syncing the client geometries with some interpolation, you can also use client side physics for interpolation. Ofc a server running everything is quite the CPU hog, so most titles do some outsourcing to the clients.
I just wonder why jme3 on the server at all?, my server only uses it for assetloading of meshes, but the rest is independet of it, as there is always a certain overhead you don't always need.
True, but in my case the client and server share a lot of code (for single and multiplayer). Also, I can take advantage of jME3's collision detection and such on the server end.
As with everything, it's a design question. For some games this may be perfect, for others it's totally and utterly useless.