Brodie,
I work with Swiss turning every day - and yeah that would actually be easy in a Swiss turn machine. It would still need to be programmed and that would be done on CAM.
I also think - if a blank was made out of brass - to length, with ID and OD turned - then the engraving could be done on a 4-th axis CNC router. NOT an indexer, which only turns some 1 or 5 degree increments. A full 4-th is a rotary axis to the machine. AGAIN - programming would be done on CAM.