I don't really see how rugby could compare, if anything we already do this to a certain degree due to the competitions in place.
In football you have teams you doing pretty well against all odds (Leicester winning the premier League being the finest example). Rugby don't have too many situations like this.
But then football has relegation in pretty much all leagues. Rugby has this in England and France. Not Pro14 for example. Then even when some teams are promoted they don't qualify due to stadiums etc. Which shows just how little the leagues change.
So yeah.... If anything rugby is a series of leagues that don't actually experience anything like football in terms of little teams making incredible league long performances. Completely different sports in completely different situations at a CLUB level. I feel like football having FA cup, League cup etc help teams have miracle moments (this wouldn't be applicable in rugby though, no. matches etc.).
International though.... Stuff like the six nations and championship make me argue it's already happened.