This article is from the Storms FAQ, by Chris Landsea firstname.lastname@example.org with numerous contributions by others.
No. Many people assume that the partial vacuum at the center of a
tropical cyclone allows the ocean so rise up in response, thus causing the
destructive storm surges as the cyclone makes landfall. However, this
effect would be, for example, with a 900 mb central pressure tropical
cyclone, only 1.0 m (3 ft). The total storm surge for a tropical cyclone
of this intensity can be from 6 to 10 m (19 to 33 ft), or more. Most
(>85%) of the storm surge is caused by winds pushing the ocean surface
ahead of the storm on the right side of the track (left side of the track
in the Southern Hemisphere).
Since the surface pressure gradient (from the tropical cyclone center
to the environmental conditions) determines the wind strength, the central
pressure indirectly does indicate the height of the storm surge, but not
directly. Note also that individual storm surges are dependent upon the
coastal topography, angle of incidence of landfall, speed of tropical
cyclone motion as well as the wind strength.