Can the sheath of nonmetallic cable be removed prior to entering electrical metallic tubing (EMT)?
The wires inside Romex are THHN type, which is okay for EMT, but you cannot use a bare copper wire inside EMT.  I would transition from Romex cable to EMT with a metal box.  Bond the bare copper wires to the box with a grounding pigtail, and add a insulated green THHN wire to continue the ground through the EMT.