I would think Locomotive/Mechanical Dept.. Usually with special movements like that they get a pre-trip inspection to be approved for movement.
Depends if they were picked up en route or at a terminal. If picked up en route, the engineer would be responsible for the inspection, but to be honest I'd bet a lot of engineers couldn't tell the difference between alignment control couplers and non-alignment control couplers or would they think to check for them. When I first started running it wasn't uncommon to get a warning on our train list that locomotives in the consist weren't equipped with alignment controlled couplers. These were usually old yard switchers like an MP15AC but you could still move it in the consist as long as it was sandwiched between two locomotive that were equipped with alignment control couplers. I haven't seen one of these engines on the property in years, although, I'm sure there are one or two on the roster somewhere.
Scott