Hi Paul and welcome!
NO!! otherwise they will continue to grow and put out shoots etc, and your heap will be full of spuds!!!
hope that helps
spuds will grow anywhere!! Even if u leave one in the ground the following year they will resprout and grow more spuds!!!
I don't put potato peelings on my heap either-they sprout too. So do tomatoes, but they are easy to spot and you can move them and use as a crop too.
If your compost heap get's hot enough, you can put anything in it including weeds but I wouldn't advise putting weeds in unless it is a large compost heap which gets extremely hot
The heat, should kill most things