Well, a month ago we were on final about 3000 AFE and we were instructed to maintain altitude and turn 30 degrees to the left for a second approach due to some activity on the runway. We had to exit app mode without using the TO/GA. And there was no single forest in sight!
I have never tried it in the real sim or plane... I may write it down on the list of things to try next sim session. Dutch roll really is not an issue with the 737. That is why they removed the second yaw damper.