if the pope met a poor version of himself would they switch places for a day pauper and the prince style and have hilarious missteps?

Of course. It is required by international law.

Sounds far-fetched, doesn't it?  But it happens more often than you'd expect. 

Remember when Pope Frank went to the jail and washed the feet of some inmates? The current prelate is not big on pomp and circumstance. I've heard he drives himself around in a used Fiat.

That was episode 23 year 1932 of The Three Stooges