Untimed Jump in Level 3?

Prince of Persia level 3 features this leap of faith

To complete, one needs to press a button 3 screens and several jumps coming from the right. This needs a rather perfect execution.

The screen above is from a perfect execution, but what if one misses the time? The floor plate necessary to reach the left ledge drops, making it impossible to reach the left ledge even if one runs 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 but caught the edge, is that state recoverable without death?