Short answer is no.
Let's digress for a moment and talk about P08s, the military issue. What most people do not realize is that the chamber date is also the first four digits of the serial number. And the letter, or lack there of, below the frame number is an essential part of the serial number. The four digits on the front of the frame roll over and there were dozens, if not hundreds, of P08s with the same four digits.
The 1920 commercials were made by DWM from existing P08 parts after the war with no chamber dates Thus its possible to have several 1920s with the same number made in different years of the 1920 run.
There was also a cottage industry assembling Lugers from ex-military parts, accounting for most of the mismatches. The cottage industry occurred after WWII as well and accoints for the occasional nickle plated Luger.
True commercial commercials used an entirely different numbering system.
You 9 mm having a 1920 "date" means it's not a commercial. The "1920" is a permission date and does not indicate the year made. The permission date pistols were intended for post war police or military issue.