Nah, it's not quite as gruesome as that I'm afraid. Basically the anticoagulants inhibit vitamin k1 which is essential for blood clotting. But it doesn't cause them to bleed from every orifice as is often thought. What happens is that during the rough and tumble of your average rodents life, they sustain minor internal injuries (bruises) through playing, fighting and squeezing through small spaces. Because blood clotting is inhibited, eventually the internal bleeding becomes so severe that they die from critically low blood pressure (hypotension). This is why it can take up to a couple of weeks for rodenticides to work. The more active (generally younger) rodents will die much quicker than the fat, lazy adults.
Still pretty gruesome mind you.
Anyway, who told you rats can't fart? Have you ever smelled a rat?
(BTW, the antidote for rat poison is vitamin k injections - similar to naloxone for opiate od's...)