The water has the added benefit of being useable for something else.
yes, the ice pack will perform the same function, but the fridge can't make the ice pack any colder than it can make the water. there is no magic to the blue fluid. It basically just freezes and thaws like anything else, having the mass in there is what makes the fridge "more efficient" versus just air. The fridge can only remove so many BTUs of heat no matter what is in it.
I personally keep my fridge full of a combination of small water bottles, juice boxes for my kids, sodas, and other drinks in 12 oz containers... Same function, multiple other uses.