During the Underground era, the East London Line closed on weekdays and Sat just after 0100. However it was self contained and didn't clash with the National Rail network as it does since the extension opened.

I'm sure if LOROL wishes to add extra services to CP or West Croydon, this would have to be planned way in advance with Network Rail, so that overnight engineering work could start later.

Now I look at it, with the 35 min gap between services at CW, passengers are still going to use London Bridge which benefits from an extra train to Victoria which maintains a 15 min service until 2352.