OF course
I'm not saying that I am in such great demand that I check company references (well I do, but not obviously) but it has come up.
I can't actually count all my fingers and toes, there's a bunch of them that's all I know. But it has happened and reading your post made me remember it. I was actually offered three jobs once day, after several weeks of hard core hunting, and I got the pleasure of replying with "Thank you for your offer but I've chosen to go with another company at this time. Hopefully I will still be considered if I feel it is a more suited opportunity in future."
What a power trip that was. It's not always that way but it's really nice when it is.