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).
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. Maybe already posted somewhere here, but it really is a pity that Bombardier/Sextant did not add some kind of auto-trim for power changes or a powerful yaw damper.
AFAIK even WW2 Messerschmitts had something like that.....