The puddle jumper photo became iconic because of who shot it, not because it was revolutionary, uniquely aesthetic, or even technically excellent. It came to represent HCB's lifetime of work at snapping the decisive moment.
So, no, an infinite number of Leica-carrying monkeys cannot reproduce it because they aren't HCB. There are already millions of "puddle jumper" photos out there from millions of unknown photographers and they are destined to remain unknown. To produce another "puddle jumper" photo, a photographer needs to establish a body of work recognized as unique or seminal. From that work, a "puddle jumper" photo can emerge as a representative icon.