The buzzer, I think it only operates above 2000 rpm. The system monitors the oil pressure at "idle" and at driving rpm and has there are different values for each and there are two sensors. The "cut-off" point is 2000 rpm. Below this speed it won't sound the buzzer because it's not reading the high-pressure sensor.
So you either have oil pressure that is insufficient or you have the wrong "high" sensor. My guess is that above 2400 rpm the oil pressure increases enough to be within the acceptable range.
What goes on that location is a 1.4 bar sensor, (or 0.9 bars I guess for some cars that we never got here). You never said what kind of car you had. You can put the 0.9 sensor back if you think that's right but I think you should check your oil pressure anyway, with a gauge, to be sure. That is the only way to know what the oil pressure really is because the VW system isn't that reliable, even when it has all the correct components.
You asked if replacing that sensor might stop the buzzer. It might, it might not. Yes, it sounds like you have the "wrong" sensor but you could have an actual oil pressure problem, or you could have a problem with the system (follow the testing procedure on that page).
If you determine that your oil pressure is just barely above what is considered minimum, I would consider trying to fix that because low oil pressure isn't good.