First of all, I do not have a Nest doorbell.
But it looks like your photo is of the doorbell chime. A typical chime will have two solenoids. When the doorbell is pressed, one solenoid is activated and hits one of the two chimes, causing the DING. When the button is released the second solenoid is activated and strikes the other chime, causing the DONG.
I do have a neighbor in our tract neighborhood with the exact same floor plan, and he has a Nest doorbell.
I suspect it will work on yours.