What should be interesting next time you fly over a tropical storm/depression/hurricane is a comparison of displayed pressure altitude and GPS altitude. I suspect that you will find as you approach the tropical storm and the air pressure reduces the aircraft will start to descend in 'real GPS altitude' which will show continually lower vertical distance above the geoid, while the pressure altitude will remain the same.
It raises the question of whether it is time to move to GPS altitudes as it would save all the real height descending and climbing but also significantly reduce altimeter pressure setting errors which are surprisingly common if ASRS is to be believed.