Well, you're taking a simple case that isn't going to be applicable across the board. You can have a highly polar molecule that isn't very acidic at all, and you can have a completely nonpolar molecule that's highly acidic. I think a better way of thinking about it would be (and I'm not 100% sure on this, but pretty confident) that the stronger hydrogen bonding a molecule is able to exhibit, the more likely it is to be able to solvate an ion. There are probably cases that fall away from that statement though, probably due to ion size and charge or something.