As long as you don't have any perishables packed in it, yes. Airline personnel will have to inspect the contents before you check it, to be sure that there is no dry ice inside. (If it is a softside collapsible cooler, you probably should not put any glass containers in it, either.)
We take our hard wheeled cooler as luggage all the time, packed full with beach toys/towels. I always put the contents into a pillowcase when I pack it, so that I can pull everything out easily inside the trunk of the rental car when we initially stop for groceries and ice.