Depends on how you define "reach". The standard definition of "reach" in the context of frame geometry is defined as the horizontal distance from the BB to the top of the head tube, so it's not dependent on your bar height. If you define reach as purely the horizontal distance between some point of reference on the frame/seatpost to some point of reference on the top of the handlebar then you are correct. If you are defining reach as the actual distance between some reference on the frame/seat (eg, the front of the saddle) to the top of the shifter hoods, then this distance will also be changed when going from a 15mm riser bar to a 0mm riser bar, but not equal to reducing 15mm of steerer spacers while keeping the same handlebar, for the reason you described. You can calculate this if you know the saddle-bar drop distance.