no, not a Dreyse number
the two Dreyse made Schrader guns in my list have a number between 37700 and 38400. don't believe schrader made or sold 16000 guns before so it must be a number of another firm in suhl/ zella mehlis.

in any case the double rifle is highly unusual and your explanation with the cheap express cartridge for everyday and the big barrel for encounter dangerous game making sense. do you know anything about the history of this gun? were did it survive the last hundered years?
the 600 NE loaded with lead bullets at 500 m/sec makes a "20 ga super magnum".