I had a wheelbarrow I was borrowing from a neighbor on a hot day, he must have inflated the tire to 120 psi on a 60 psi rating, he was that sort of guy...
It was sitting in the sun while I was working on something and BOOM!!!!! I though he was setting off fireworks or something to be an ass, I nearly had to change my underwear... I went to use the wheelbarrow and half of the tire was torn to shreds.
The weaker tire as a result of heat and the higher pressure caused it to pop, so yes, it is possible.
I doubt that with the volume of a skinny bike tire it will result in the same sort of failure, especially on a "good" tire, but if there's an underlying issue, you may discover it in an unpleasant fashion...