"What happens when you chamber sleeve a 16 to a 20 ga? "

"chamber sleeve" is a good term. By analogy, Brownells sells "choke sleeves", not "choke liners" for the muzzle end.

"1. How will this affect the pattern?"

My guess is....not in any statiscally significant way. And it would be extremely difficult to design a really definitive experiment. It would be relatively easy to do if you were just enlarging the bore because you would test the exact same shell under controlled conditions before and after the bore enlargement. But in this case you'd be patterning a 16ga shell first and a 20ga shell later, which introduces a lot of other variables.

"2. I'm assuming this means the whole barrel is considered
backbored?"

Actually, to be more precise, it's "overbored." Since we have two terms, seems they ought to mean different things. Some accept the distinction that "overbored" is a larger than standard bore from the beginning while "backbored" implies a post-manufacturing enlargement.