We planted 4 50 foot rows of potatoes this spring. Northern Reds (2 rows), Kennebec, & Yukon Gold. We've been eating off one row for the past month. Dug the rest today and weighed 320 lbs. The Northern Reds produced the most and the biggest.
The only reason I know to let potatoes "rest" is after they are washed before they are stored for the winter.
When you wash them, they need to dry so the skins toughen for storage. The reason you wash them is to make sure that the dirt is washed off to help them keep longer.