What a fascinating question.
I like to think about it this way. The atmosphere exerts a certain force on the surface of the earth. That force is caused by gravity pulling on the mass of the atmosphere. This is known as the weight of the atmosphere. It is this weight that causes sea-level atmospheric pressure to be what it is.
If you picture an aircraft sitting on the ground, the total weight of the atmosphere plus the aircraft will be the same as the total weight of the atmosphere plus the aircraft if the aircraft is airborne. However, in the airborne case, the atmosphere must transfer the weight of the aircraft to the surface rather than the aircraft's wheels. The only way the atmosphere can do this is to increase its MSL pressure slightly.
The bit where I get stuck is that the atmosphere doesn't have a "lid". If you kept pumping air into the atmosphere (from a hypothetical worm-hole), I don't think it would increase the atmospheric sea-level pressure. The excess air just escapes out the top into space.
It that is true, does getting an aircraft airborne actually increase MSL pressure, or does it just displace some air out the top into space?