Howdy Erinn! So excited for you!! It will be so much fun for you to be at Walt Disney World Resort over the 4th of July holiday!!
Disney's Old Key West Resort is wonderful!! It's a peaceful tropical paradise!
The answer...YES! You can absolutely enjoy the amenities and recreation at the resort until it is time for you to depart. The only "challenge" is that there aren't any showers or facilities for you to freshen up. You will be able to use the public restroom facilities and you might talk to one of the Cast Members at the resort as they might have other suggestions for you as well.
Have you stayed at Disney's Old Key West before? It's lovely and I'm sure you will find plenty do to keep you busy throughout the day. You are also just a short water taxi ride away from Downtown Disney where a world of shopping and dining are available for you to enjoy.
To ensure that you continue to have access to keyed areas, don't go to the front desk and close out your bill at check-out time. This will also allow you to continue to charge meals and snacks to your room if needed. Before you depart, you can go to the front desk and close your account at that time or your account will be closed automatically by Disney at the end of the day so that you can continue to enjoy your vacation until the very last moment.
So so excited for you!! I have never been to Disney World during the 4th of July. I know you will have a magical time!!