Yes, because the application you submit is what is updated in Common App. They get a pdf copy I believe.
So as you change it, it will update for the next school.
But why in the heck would you do something so craz?. The answer to the prompt is the answer to the prompt. And while no one truly knows, at many schools, the essay may not be read…or read in huge detail.
And you’re putting an awful lot on yourself requiring edits, re-reads, more re-reads and I can’t think of a possible reason why this would be a good idea.