Your biggest issue is the mechanism to convert the mechanical energy of pulling the lever into the rotational motion of the propeller. This isn't impossible, but it is rather inefficient.
At the beginning of the pedal stroke, the foot is stopped but the output shaft is moving at full speed. It takes a portion of the pedal stroke for the pedals to catch up to the output shaft and during this catch-up phase no force is being produce and, as a result, no power is produced. Both the Dragonfly and the Harris Vertical incorporated cams to gear up the pedal stroke in the beginning to allow the pedal speed to more quickly match the speed of the output shaft. However the cam must be designed for a specific gear ratio. So on the Harris Vertical, the cam will only be effective for around one gear selection.
The Alenax Trans-bar bicycle was commercially produced in the 1980’s.
There is an entire blog article here outlining all kinds of variations of linear to rotary drives, one constant when looking at the descriptions and illustrations is how complex most of them are.
Try working out the mechanical system on this bike....
This brings up the second issue, mechanical advantage. Your pulling on levers (or even peddling on a conventional bicycle setup) is unlikely to produce the proper torque and rotational velocity for the propellers directly. You will need a gear train or something more exotic to translate the movement you make into the proper rotation for the propellers. This is generally done with a gear train or transmission, and it too will add weight to your airplane, making it more difficult for the human power plants to actually propel it through the air.
Looking at real human powered aircraft, you will see the two common factors are extreme lightness and fairly extreme wingspans. This is to maximize the rather tiny amount of power a human being can actually produce, and allow for control flight (underpowered aircraft are generally good at uncontrolled flight, and usually straight into the ground).
A typical human powered aircraft
So the short answer is, your design is rather implausible, and would need considerable rethinking to become an actual, flyable airplane.