Its all down to angle of attack. If you get enough Alpha and enough power it will fly. (you must have experimented with your hand out of the car window)
Before the aerofoil was discovered planes had slab wings (ie flat, no curves) and they flew. The curvey bits just made it more efficient.
Some aerobatic planes (eg Extra 300) have symetric aerofoils ie not as efficient the right way up but not quite as inefficient the wrong way up.