You are authorized to fly instrument approach procedures without either paper or electronic (EFB) charts?
Not on a routine basis, only if both EFB become u/s during a flight and under certain circumstances out of base, however in practical use that is impossible as all weight and balance as well as performance calculation is done on the EFB as well.
Major chart cycles are every 56 days with an interim update cycle, thus a database change every 28 days. It's not possible for database vendors to have a database ready 27 days before its effective date, at least not that I have seen. In my current work I receive a world wide nav database typically 14 to a maximum of 17 days before it becomes effective.
Yup, still more than enough time to distribute it even through a large fleet. Even more possible if you do not need a worldwide database and therefore get your update cycle even earlier.