The back fork should be connected to the seatpost with a pair of horizontal braces.

It's an exaggeration to say it would immediately break. But if you put weight on it, it will tend to spread out (imagine putting weight on a bent piece of metal shaped like a ^). Still, the front fork isn't braced, and bikes exist with quite a large rake angle on the front fork (think a Harley-Davidson style chopper). So maybe you can make this design strong enough to bear a person's weight.