This is your standard refrigerator ice maker. It would not make enough to fill a cooler. We bring along a few ice trays because it tends not to fill up fast enough for our thirsty family of six. We also usually keep a bowl of ice in the freezer as the trays freeze up.
For the cooler, I freeze water in 2 liter soda bottles or plastic milk jugs and use them in the cooler. They stay frozen longer than ice cubes. You could still throw a ziplock baggie of ice cubes in if you just wanted some for drinks. If the cooler is smaller, you could use the smaller water bottles to freeze. The refrigerators are full size, so plenty of room.
I've never run into an ice machine at the resort, but there might be one. You could call and ask them.
Sheila