Yes, they can go to the house. It's abandoned and has fallen into disrepair, so entering won't require any effort. Inside, they'll find that the house has been cleared of any personal belongings. It seems the family really did move out.

Closer examination will uncover a tree around the back with the name Esmond carved into it. Underneath that is the name Lorelai. It's possible the woman remembered the name "Edmond" incorrectly. Recent disturbances to the land from the blights has caused a small box buried beneath the tree to surface. Himeka and Jeremy can dig up the box. Inside are items of no real value, but which were evidently important to their owner such as marbles and pressed flowers. It also contains a few notes and letters from Josselyn over the years. The letters don't reveal anything important, but they establish the two as long time friends.