Paul, I had this question from a lady today in fact, even though I don't do this work, she has an "exterminator" and was wondering.
I can tell you, we have bait boxes out the wazoo at most residences and businesses, especially with folks thinking all mice carry plague
and hantavirus as they've been told by the internet experts.
My only experience is observational and has been, the clients with heavy baiting programs have dead mice in their yards and landscaping.
People with a water source seem to have accumulations right near these water sources (of course I'm in the desert so figure that in to the thirsty
dying critter hypothesis).
Then we have the folks who call to get poison bait chucked into their attic and call me about 3-5 days later when they "smell something funny."
Guess what?
It is dead mice!!!

That usually ends that type of treatment for those clients and they look for mouse trapper folks, non toxicant style.
The secondary toxicant issue has been discussed, we all know the LD (lethal dose) is made for the critters like mice and rats, but of course that doesn't take into account the lab breed dog who eats everything he can and the owner who has a major mouse colony and has dozens dead quickly.
It seems after all the stories and speculation, the only folks who usually find dead pets due to bait is when they have direct access to the bat itself, which the bait stations as we know are meant to reduce or eliminate.
In summary, I believe they die either near water or shelter, but some likely die in between. I would also say it depends on the type of bait used and the mode or mechanism by which it causes death.
But......
I'm no rodent guy, so everything I've learned was through Purdue IPM course, PCT rodent manual and the WCT conference two years back in Vegas.
Justin