Yes you should be able to access your premium account on the sp server. You have to ask an admin to unregister the nickname for you, because the account can be considered as stolen as the person does not own the premium account. The real owner is you so you should be able to join with your nickname even if it is an sp server.
ImWaterMelon you have a point however, this is not how it usually works, because if you own the premium account, that account is only yours, someone else cannot use it as it can ruin the actual player's reputation and more.