Can making seawater drinkable quench the world's thirst?

Sure, but water recycling is even more efficient. You can extract pure, drinkable water from used shower water, or even toilet water, using much less energy than it takes to remove sea salt (since you're fighting a much gentler osmotic gradient).

Psychologically though, I think most people prefer the idea of purified sea water to purified toilet water ... even if the sea is a toilet for everything that lives in it!

Would there be any logic in solidifying NaCl for fuels or for burning to drive electric generators?

You can't burn NaCl.

Fluorine disagrees.

People can be persuaded otherwise. They had no problem drinking tap water until water bottle sellers told them otherwise.

Additionally, desalinating water provides more water to go into the water recycling process, without needing to wait for rain.

I'd like to know the impact that the desalination plants in Israel and Saudi Arabia have on the environment, specificially the sea life in the water being sucked into these plants. It's my understanding that the biggest hurdle for desalination in California is not energy but the ecosystem.

What a silly question. Of course it can.