The easiest way to do this is to make your backups the mechanism by which you refresh your Dev/QA environment from Production. It means your Ops team are very nearly doing a DR exercise every week.
It's a great idea, we were doing that at my old company a few years ago. It also means that you have fewer problems with migrations when pushing them out to production.
I know lots of companies doing TDD but that have never done a full test restore from their backups.