A few problems: The pressure behind the prop is HIGHER than in front, and higher than ambient, until equilibrium is again reached. The amount of thrust generated depends on the pressure rise (delta p) times the area of the propeller disk. The Bernoulli effect is seen at the front of the propeller disk, where the pressure is lowest.

Why would you suspect a decreasing pressure differential to cause more air movement as it dissipates? Decreasing pressure differentials are approaching equilibrium, and momentum change is decreasing.

With the bathtub vortex - you seem to be ignoring the sustained pressure difference set up by the drain itself that sustains the vortex. I see no applicability to the propeller, except that they rotate like tip vortices, which decrease in intensity with time and distance from the energy source - this effect has been measured by NASA, and agrees with theory.

You are invoking magic again.