No the supermarket is next to Hyatt which is the start of the downtown area. There is a closer supermarket to the Mayan which we did not use plus there is a small store at the Mayan where you can get some items such as bread, milk etc.
Costs a little more but cheaper than getting a cab just to get a couple of items in the middle of the week that we ran out of.
Have a great time!!! You will love the Grand Mayan it is a fantastic resort!!!!