That has always been my fear too. 15 years of poison use here every fall without any problems. The rats usually die deep underground and I don't smell anything. I do a daily look around for carcasses when the poison is out. I have only seen 2 die out in the open. We use the tomcat brand in a bait box hidden under some hay bales or behind boards so no one can get to it but rodents.One of the reasons I'm hesitant to use poison is because I don't want them to die under the coop and have it stink horribly. I'm also concerned about our dog (or even the chickens) possibly being poisoned by eating (or pecking) a dead rat. I've heard there's some kind of poison that isn't harmful to other animals that eat a rat killed by the poison, but don't know what kind it is.
Do what you are comfortable with. I'm not necessarily comfortable using poisons but it is all that works here. The rats that come into my shed are voracious, digging long tunnels and consuming a lot of feed. I don't generally see them just the damage and increase in feed.