No.

A watch winder is not required for the normal operation or maintenance of an automatic watch.

If the watch is worn regularly, normal wrist movement will provide the energy needed to keep the movement running.

A watch winder may be convenient for collectors who rotate between multiple watches and prefer to keep them running when not being worn.

Using a watch winder does not improve accuracy, increase longevity, or replace regular servicing.

Whether stored stopped or running, a watch should still receive periodic maintenance according to the recommended service intervals.