Nothing different would have happened. Henry told the Pope to piss off and married his second wife, Anne Boleyn, anyway. It might be more interesting if you had asked what would have happened if Henry had caved in to Rome and stayed with wife #1.
When you can't get what you want from the Pope, start your own religion. When you have everything you want because you are rich, trade places with the jester and the pauper? Yeah right. That only works in fiction.
