I grew up hunting with a 16 gauge model 37. It is a fantastic shotgun. IMO, a handgun is the best tool for clearing a house. It's short and can be operated with one hand. But if am barricading myself in a room waiting for the cops to arrive, I'm grabbing a shotgun. I don't care what length or gauge it is. $200 is a good deal if it's in decent shape. If he decides he needs a short barreled, pistol grip 870 in the future, it sounds like he should have no problem getting his money back from some of the members here.
I love the Ithaca 37 shotguns. Once broken in and well-lubed they are nearly indestructible. Even in ugly conditions they can keep going and going. Even in 20ga, with the right load they should be plenty for basic home defense, yes. I'd prefer the 12ga variant myself, but an I37 in 20ga is a great option.
If the interface/controls please you, as compared, say, to the Mossberg 500/930 and Remington 870/1100 line, go for it.