can the autopilot on a transport jet fly a DME arc
Yeah they can and they do it with a slight constant bank all the way round to the lead-in radial.
does it involve some level of involvement from the pilots?
Only to programme the FMS. If its already in the database then its just a matter of going to the arrivals page, line selecting the arc procedure and hitting enter.
You could always put it in HDG mode or even hand-fly it I suppose.
