No; they print them at their warehouses on an as-needed basis. DVDs get destroyed and lost easily, and they don't cost much to print. Individual machines will still run out if they're not restocked, though.

If it's true, they probably use a system similar to library ebook loans. They have a certain number of licences that can run out, even though there's no technical reason for it. I don't know why copyright owners would do it with Redbox since they get money for each loan.