Stu,
Even if sea water density was significantly changed by pressure, which it is not, changes in atmospheric pressure are not transferred to the sea bed.
A fall in air pressure produces a sea level rise to compensate.
A barometric rise causes a sea level depression to compensate.
You can not have adjacent areas of sea bed with different hydrostatic pressures without creating a flow of water to even them out.

You tell 'em, Stu. In the end, real science will always win out.

He got it wrong Steve.

Wind however can produce such effects because the compensating flows are slower.