seems like 3 scenarios...
You didn't mention the airplane but with the loss of an engine, you will lose that source of electrical power and then what happens to one of your autopilots. Do you lose one autopilot? If your CAT II procedures are predicated on two autopilots, you are committed to a go-around.
IF it is just a Cat I approach, our procedure on the 737 was to retract flaps to flaps 15 and continue the approach.
IF the failure occurs before 800ft, one argument would be to sort it out before attempting the approach. Below 800ft, just retract flaps and continue.
But other circumstances would influence the decision such as airfield, runway, terrain (approach and go-around), etc.
Good topic for discussion...