The autopilots on the Q300 and Q400 are simply not certified for single-engine operation (which is a pity as it adds quite some workload when things are sh*tty anyway).
They can be used in the cruise on one engine. It's only the approach that they aren't certified for.
I personally doubt that the Q400 autopilot can fly a single-engine approach without any difficulties as the Q400 requires rudder trim changes for any power change and the autopilot simply cannot trim the rudder.
How is this different from a two engine approach? Any flying on autopilot in the Dash 8 requires retrimming the rudder during power changes. So an approach on two engines requires trimming as well. I sometimes use the rudder pedals myself in turns because the yaw damper doesn't do enough.