He doesn't necessarily learn anything regarding the Restricted Section in his conversation with Harry; however, immediately after his conversation is probably his best chance to have McGonagall listen to him about the Restricted Section.

Dumbledore and McGonagall don't really have very many options to cheer Harry up. It's suggested that they already tried other students. Regarding friends, his closest would be McGonagall and Quirrell, neither of whom worked, Hermione and Draco, who are both inaccessible for obvious reasons, and his parents. Of all of these, the last seem like the best option. This is particularly so considering that Harry would very likely want to shield his parents from his present emotions in a way that is not true of Dumbledore and McGonagall. We can debate how well it would work, but short of explicitly using magic on Harry (which might not even be possible, now that he's an Occlumens) it's the only thing McGonagall and Dumbledore could do that would have any kind of chance of success.