Picture the downward force generated by sitting on the bicycle causing the rear axle and bottom bracket to spread away from each other, causing the seatstays to break at the seat tube. This is what chainstays prevent on a complete frame.
Though when you start to pedal, the chain would tend to pull in and bend the seatstays, but there should be some level of force that is less than the opposite force caused by the rider's weight, so this bike could work under light pedal pressure.