I have operated the 737 for four operators, three British and one Irish. All have a minimum disengagement height of 158' from a coupled ILS approach. Autopilot used is not permitted below MDH for non-precision approaches.
This means an approach to Cat II minima would have to be done with both channels engaged. Manually landing from that would be foolish as the nose will have been significantly trimmed up at 380' radalt - manually flaring a severely out of trim aircraft in marginal visibility, especially on short, wet runways with any cross wind would be a handful and an unwarranted risk. It's manageable, but it's best to let the autoland do its job, so you fly the approach like a Cat III but use the Cat II limits - the airport would be in LVPs anyway.