Most airlines will not keep your luggage checked in at the airport overnight (unless they have to e.g. missed connection). That rule of thumb applies to normal-time departures and that hypothetical 1am departure as well; you generally cannot check in if the luggage has to be kept by the airline overnight. (Some airlines/airports do not follow this; it is merely a rule of thumb.)

There may not be a specific written rule, but there is no need to get into a theoretical discussion of whether a check-in at 2am is overnight, and so forth; common sense serves as a reasonable guide. You can check in the day of the flight.