It does create additional pressure. I think the real question is if that pressure is in any way detectable. Think aeropress vs. French press. The pushing in a french press simple separates the particles, while the aeropress is indeed squeezing the water through the filter.

Maybe the pressure isn't directly having an effect. But a side effect is that you stop the brew process after a short period of time and that will have an effect on taste.

There is. What effect that has is an interesting question.

Aeropress FAQ:

"The AeroPress filter is 2.5 inches in diameter so the area of the filter is 4.9 square inches. If you press down firmly on a scale, it is relatively easy to get the scale up to 25 pounds and then if you press hard on the scale, you can certainly get it up to 50 pounds. Therefore if you press similarly hard on your AeroPress while brewing coffee, the firm pressing will be at 5.1 psi (25 lbs/4.9 sq in) and the harder pressing will be at 10.2 psi (50 lbs/4.9 sq in). Since a bar of pressure is 14.7 psi, the former is .35 bar and the latter is .70 bar."

https://www.aeropress.co.uk/pages/faqs

See also James Hoffman's experiment:

https://youtu.be/jBXm8fCWdo8?t=976

Espresso requires a multiple of that— 9 bars minimum if I recall correctly.

I know. I said that in the comments below.