Yes, by measuring the pressure at ground level, measuring the pressure at the top of the building and then applying the correct formulae (unbeknownst to me) for atmospheric pressure changes in relation to height to the difference in pressure, you could come up with a reasonable estimate for the height of the structure. This is exactly how an Altimeter works, by the way.

It is also worth pointing out that this exact same node is to be found under Niels Bohr and in a much more accurate recounting of the actual story too, I might add.