I expect it to work the same because charge path and discharge path stay the same. Left side of the potentiometer for charging and right side for discharging. When charge resistance grows the discharge resistance decreases. I don't understand why you would need diodes and also that bridge between them.Why would you expect it to work the same with or without diodes?
The diodes isolate the charge resistance from the discharge resistance so that the two can independently control their respective times.
Without the diodes, the two resistances interact such that the full duty-cycle range cannot be achieved.
