I believe that this is a requirement of Bernoulli's theorem
Not really. Bernoulli's theorem deals with the variation of pressure and velocity at different points within a fluid. It's not really a system level thing, but a characteristic of the Euler fluid. It's certainly not necessary to demonstrate a system as closed with respect to mass flow to apply Bernoulli's theorem -- that would be somewhat difficult in that its prime purpose is to relate the properties of the fluid at different points on a streamline.
If there is a force on the ground, is there also a rise in local air pressure, if so does this imply a rise in pressure under the wing which would also contribute to the lift. Presumably, if the force on the ground is equivalent to the weight of the aircraft there would be no need for a reduction in pressure over the wing c.f. the hovercraft.
This all depends on where you draw the arbitrary boundary around your "system". I think that, in a sense, you're double-counting.
The air is merely the medium through which the ground supports the aircraft. The ground applies a force to the air. The air applies a force to the aircraft.
In the same way, when the aircraft is parked, the ground applies a force to the tyre. The tyre applies a force to the aircraft.
But that doesn't mean that there are no stresses in the tyre, does it? To apply the upward force to the aircraft, the tyre must deform around the wheel, creating more pressure on the lower part of the wheel than on the upper. In the same way, the air "deforms" around the wing, causing the pressure difference we're discussing. The fact that the ground applies a force to the tyre, or the air, doesn't change that.