Is it possible to maintain horizontal flight with the angle of attack above critical value by increasing speed? In this video a stall happens at 1:40 upon reaching the critical angle of attack. The air flow is now detached from the upper part of the wing, resulting in higher pressure above the upper part of the wing, thus eliminating the major factor of lift.



Let's imagine that we have extremely powerful engines and enough tail stabilizer authority to maintain horizontal flight with any speed. 

Is it possible to maintain horizontal flight when:


wings have high angle of incidence (let's assume some experimental design)* 
aircraft has zero pitch condition (straight and level flight)
permanent state of high angle of attack (as the consequence of the 1 and 2)


*high angle of incidence is an angle between wing chord and longitudinal axis of the plane (fuselage)

I assume, the lift that we will get in this case, will be generated mostly by Newton's law by deflecting air ONLY by the LOWER side of the wing.
That is kind of what the mechanism of lift of a flat plate does: the sharp leading edge destroys the upper flow pattern almost immediately. This question has more info on it.

The lower side of the wing does provide as much or more lift, even when stalled, at AoA of 45°, so lift would not be the problem. Drag would be: 

Image source

On this scale, drag for the NACA 0012 profile is very close to zero until the aerofoil stalls, after which it jumps up and continues climbing. At AoA of 45° the C$_D$ is 1.1 instead of about 0.02 when not stalled - you need over 50 times the thrust to maintain the stalled condition you are describing!