Is Autopilot engaged when an engine failure above V1 occurs on modern airliners?
Most non-normal ops in an airliner follow the same concepts for light aircraft - make sure the aeroplane is under control and following the desired flight path before you do anything - which includes engaging an autopilot. 

So for the Boeing aircraft I fly, ensure you've got a positive rate of climb, speed should be V2 - V2+15, ensure the aeroplane is in trim (pitch first, then rudder) and your following any prescribed engine failure routing. 

In terms of autopilot use, part of our company SOP is to engage the autopilot at 1000ft AAL, this is not to relieve the pilot of the responsibility of maintaining control - it won't control the rudder - more to reduce the immediate workload and allow more effective management of the non-normal situation. Once the autopilot is engaged the aeroplane can be accelerated, flaps retracted and any non-normal checklist completed.