Can you recover from failing the timed jump in level 3 of the original Prince of Persia?

Level 3 of Prince of Persia features a leap of faith, where to complete, one needs to press a button three screens and several jumps coming from the right. This needs a rather perfect execution.

What happens if one misses the timing? The floor plate necessary to reach the left ledge drops, making it impossible to reach the left ledge even if one runs another cycle and re-opens the door. Death would reset the plate, but is undesirable. One can technically catch the edge, but the gate closes, above.

Is a failed timing of the jump where the player caught the ledge recoverable without death?