Technically no, you would need to be staying at the resort to use the beach house facilities. If you drive you will also need a way to get past the guard house in Palmetto Dunes on your way to the beach house. Those staying at the resort are provided parking passes so they just wave you through.
However, given the fact that the beach house sits next to a public beach you can easily walk up to it. The only real security are the keyed gates on the 2nd floor as you walk up from the parking lot/garage and/or beach.
The same is true for the resort itself. The only security is the electronic gate arm as you drive across the entrance bridge. You would normally use your room key to get past that. However, since the resort sits at Shelter Cove with dozens of public shops and restaurants around you can easily get to the resort without a car.