I don't think HVAC systems will do much damage there. I have a gadget on my airplane that gives altitude accurate to the foot, and that's while moving 60MPH or more through potentially turbulent air.
I am thinking more about actual differences in atmospheric pressure between indoors and outdoors, or even between rooms in a building. If the ventilation system is installed correctly this shouldn't happen, but if it is not then you can cause either an overpressure or underpressure in the building.
I don't think buildings will sustain much of a pressure difference. For example, a 10ft-equivalent pressure difference will exert a roughly 16 pound force on a standard residential door, which would be highly noticeable, and it's probably tough to seal a building well enough to contain that kind of pressure.
