Modern pool heaters can get the water up in the mid-80s pretty quickly. I've had both heated and unheated pools at my homes, so I do know a bit about it. Would I go in water that's 77? Sure, because to me that's not cold. I much prefer temps in the 80s - 84 is just about perfect - but 77 is pretty close. If the air temps are about the same, there's a breeze and no sun, it would be chilly for a few minute, but still warmer than the ocean and the Med in late May is already fairly warm.

A couple other random thoughts on this. One, it's Greece. It's not a great country for customer service issues at hotels, at least in my experience. Two, it's Greece. Why waste time at a hotel pool when you could be out on the island? Three, if you're looking for a swimming spot for your kids, a $500 a night hotel is a pretty expensive way to find them a pool.