Rat poison usually reacts to the stomach acid in their system. They eat it, then it gets wet.....once that happens it basically causes internal bleeding and ruptures within thier blood vessels. This makes for a clean kill because the poison has chemicals that keep the rat's blood from clotting properly.
There is an antidote for rat poison and that's vitamin K....you'd normally receive a shot from a doctor, but then get a prescription for daily doses until the body heals.
As for the snake, it really depends on how it digests the rat and how much of the poison the rat digested. I would expect that the snake would either get sick or die, but there are no guarantees. Snakes are extremely interesting animals. I've skinned a rattlesnake while it was still moving......one of the freakiest things I've ever done. I had chopped its head off and it just kept moving around....after skinning it, I could look in its rib-cage, which extended the lenght of its body and could see its heart still beating and all of its organs. Snakes freak me out...