denti:
Our 737 MEL has therefore an entry that allows all nav databases to be out of date only if there is no requirement for any RNAV procedure or navigation and of course as long as you have current charts on boards (charts are no longer required in dual FMC installation with EFB installed which may be inoperative as well). If you want to use any kind of RNAV procedures, no matter if enroute, approaches or departures, you need at least one current nav database on board and usable for the crewmember responsible for navigation.
You are authorized to fly instrument approach procedures without either paper or electronic (EFB) charts?
To be honest i have never seen an out of date nav database in airline operation on the 737 so far, with good maintenance procedure and the possibility to pre-store the next database up to 27 days prior the date it becomes active it seems easy to keep them current.
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.