Can this design provide more lift force than thrust from engine?
Because there is no free lunch.  A single wing behind a propeller or a fan can see some amount of performance gain from being in the propeller's slipstream, but, when you start stacking multiple wings together...it gets a little trickier.

A single wing can get an advantage from the swirl induced by the propeller, in addition to the increased speed you've remarked upon.  In a thesis written by LLM Veldhuis on wing propeller interactions, he notes that, when you have a propeller operating in front of a wing and rotating such that the inboard blade is always moving up, it changes the local angle of attack on the wing behind the propeller.  This modifies the lift distribution (notionally shown in the figure below) and ultimately decreases the induced drag of the wing for a given operating lift coefficient.  A set of experiments by Witkowski et. al. (Propeller/wing interaction) in the 1980s recorded a wing seeing up to 40% savings in induced drag based on the adjustment of a tractor propeller's rotation rate!



This is what I've, at least, seen cited at the most prominent effect of having a tractor propeller in front to of a wing.  If you have a small enough wing, though, say on the scale of UAV, there's a good chance you could have a significant portion of your wing in the propwash, which can keep the flow attached to the wing at higher angles of attack, letting you, potentially, keep a control surface or two unstalled and able to maneuver the aircraft when they normally wouldn't.

However, that's not lift, and it doesn't quite answer the question about the multiplane setup.  The problem with stacking wings so closely to each other goes back to investigations in the 1920s and can be most easily explained, I think, with the venturi effect.  When air is accelerated by the curvature of a wing, the static pressure decreases and you can a suction force, which, on the upper surface of a wing, translates into lift.  However, stack two wings (or other objects) closer together (as in the picture below), and you get something...not so good.  The image below is from a conceptual rotorcraft design submitted by the University of Maryland for the 2016 American Helicopter Society Graduate Design Contest and is a kinda strange thing called a quadrotor-biplane-tailsitter (we named it Halcyon).  However, the upshot of the image (which is colored by local pressure -- the more negative the Cp, the lower the pressure) is that, due to the wings and fuselage (the bit in the middle), you are playing a game of diminishing returns.



While the bottom wing sees very high velocity air going over it, leading to very high lift, that same low pressure zone also generates a strong downforce on the fuselage, effectively mitigating a lot of your lift (the design team estimated that it killed almost all of it, actually) from the lower wing.  The upper wing, since there's a little extra space, isn't as effected by that same phenomenon, so, in the end, the aircraft had enough lift, in theory, to fly...but it's not an efficient configuration at all.  The same would be true for a stack of wings.  In a 1923 paper by Max Munk entitled General Biplane Theory, he estimates that, in order to minimize interference effects between wings, they should be spaced apart by at least 3 chord lengths.  That would easily move your wings so far apart that not even two wings could easily stay in the propeller wake...at least for full size aircraft.