I doubt this would be a huge issue given that Microsoft has been replacing consoles that Red Ring years after they were purchased, but still, it's possible. I would be more concerned that a used console probably won't be eligible for Microsoft's warranty which leaves you with whatever the store will give. Given that the failure rate isn't blown out of proportion when talking about the older versiona of the console (though I bet Microsoft wishes it was), you need a warranty with a used one.
Unless they're willing to cover it for a few years at no extra charge it isn't worth the cost given the newer 360's aren't a lot more expensive than a used one with some extended warranty, and they're a lot less prone to failure.