From everything I have seen on the Celebrity website says that you can use the drink package on the island.
the packages pre-purchased or have chosen on the ship will be reflected in the bars and restaurants on CocoCay. If you’ve chosen All Included, you can enjoy cooling tropical cocktails, cold beer, and wine to your heart’s content.
Also it works for the wifi:
CocoCay has the same fast Wi-Fi as you’ll find onboard Celebrity’s ships, with different speeds available according to what you’ve purchased; for example, if you have chosen All Included, you will automatically be able to access Wi-Fi on CocoCay. Service may be limited on some of the beaches, but you should nonetheless be able to start uploading envy-inducing Instagram snaps as soon as you step ashore.