To clarify my answer- Yes, the airlines will accept a soft sided cooler as checked luggage.
Yes it can be filled with bottled water and snacks as you were asking.
Now I answered yes you can because I know you are a reasonable person who will pack your cooler with common sense. (All us Disers have common sense

)
I realize there are plenty of people out there who don't pack carefully but it isn't just in coolers. I have seen rotten fruit and unsealed red fruit punch containers in regular suitcases and yes, these things leak on other's luggage.
I have also seen an entire deer head- still bleeding in a cooler but it was properly saran wrapped and nothing was leaking.
I was more answering the question of whether it could be brought on or not. Not debating if its a good idea or not.
Basically, the airlines will accept *almost* anything. Look around at some of the other luggage next time you're at the airport. You might see the other 30 coolers that will go onto the plane with yours along with the duct taped boxes that one family uses because they cant afford suitcases. They will sit next to the thirty foot long tube that holds pole vaulting poles and the sports equipment for your MLB team that just went down to spring training. Oh, and that fancy Louis Vitton could be placed right on top of that trash bag holding the sleeping bags-the one that had the giant roach climb out of it. Unfortunately that is the reality of flying. Not everyone thinks or is considerate of others.
OP- the best way to take water is if you can leave it in its original case, still shrink wrapped. That will help keep them from being crushed and it adds stability to the cooler. The other poster who told you to put them in a trash bag was right on track. If you pack towels for the pool, you can also put them around it to cushion. The bags get banged around quite a bit so you would have to judge how sturdy the cooler is.
Have a great trip and don't stress too much over it. Hundreds of people do it every day.