Refrigerating potatoes is OK but not recommended.
Although refrigerating the potatoes helps the potatoes last longer the potatoes can become soggy due to the moisture.
When the potatoes become soggy due to the refrigeration then they will get mushy and not be as tasty but they will still be good to eat.
It's best to just store the potatoes in a cool dark place to keep them good and eat the potatoes up before they have time to spoil.
It's not really a good idea to stock up on potatoes because potatoes need to be eaten pretty fast to avoid the potatoes spoiling.
Depending on the climate the potatoes last between 2 weeks to a month but sometimes the potatoes can last for 2 to 3 months.
However it's best to only buy enough potatoes that you can eat and then eat those and get fresh potatoes again.