Tonight I am catching the N770 Flixbus from Antwerp to Copenhagen. Apparently it doesn't stop between Eindhoven and Copenhagen. Do the night Flixbuses to Denmark typically go via Puttgarden-Rødby, requiring passengers to step out on the ferry, or can I expect to sleep through the night?
The FlixBuses to Denmark from Germany do indeed generally* take a ferry from Puttgarden to Rödby.
The ferry departs every 30 minutes and there is a passport control so you have no option sleeping through.
Once on the ferry you are required to leave the bus. You can sleep in various places on the boat but keep in mind that the driver will not wait for you - immediately go to the bus when such instructions are announced, about 5 minutes before arrival.
*Changes in traffic could cause the bus to take another route. This could for example be ferry departures, accidents, weather etc.
It may not.
Apparently (at least tonight) the N770 line Paris-Copenhagen in particular does not take the ferry route via Puttgarden-Rødby, but rather crossed the Danish border at Padborg in Jutland. There was indeed a quick passport control there around 5 AM, but there was no need to exit the bus.