Excellent drawing/photo but the challenge is to have the cranks suspended therefore it seems you have to have split cranks and some form of transmission from cranks to wheel so that the seat to cranks relationship remains constant and only the wheel travels up and down.Anyway your drawing/photo thingy looks great.
As it is the wheel would not spin in relation to the cranks when the suspension is compressed. If you geared it up the wheel would turn in relation to the pedals when the suspension moves.
How the system would work is basically the gears and suspension make an isometric triangle. When the suspension compresses the part that sticks out has half the vertical movement and moves out a bit in an arc.