Uh, yes and no. What do you mean by "fly"? Do you consider a hovering plane to be "flying"?

If the wing must produce the lift via traditional Bernoulli effects, as opposed to the engine holding the plane in the air, then no, it won't work. The screen allows air to pass through it, so you will not get the Bernoulli effect velocity profile and pressure delta needed to move the wing upward (i.e., lift). It might be simpler to imagine what would happen even if you could get a pressure delta between the upper and lower surfaces. The higher pressure air would simply pass through the wing to the upper surface, without taking the wing with it. This all discounts the fact that the screen will have some miniscule resistance to air passing through it. In theory, I guess, you could get the thing to produce enough lift if you could get it moving fast enough, but that couldn't happen in reality, because the engine you would need to do so would make the plane heavier and require more lift... (a never-ending death spiral as we say in the design world).

Like you say, though, a brick can fly- that is, made to stay airborne- with enough engine. It's just another physical way of getting it to stay there- no wing lift, just engine thrust.