Yes, I like that he had hidden this but opened up to her, and that he knew and was honest about the fact that this is not normal, healthy behavior. When we first heard about the storage unit in the taping, I joked that he would probably say something like he wanted to give The Smithsonian a head start for its eventual Sheldon Cooper wing.
It seems like just the arrogant way the old Sheldon would respond to something like this coming to light, but he's grown and matured and because he loves her so much and trusts her (well, with a non-disclosure agreement - yes, he's "still Sheldon," thank you very much, writers), she gets to see who he really is, AND he really cares what she thinks of him as a result. Love, love, love.
And yes, I agree with much of what wowbagger said, but I think so much of the theme of Sheldon in the show has been about him learning to trust. Yes, of course he had a million and one quirks/phobias/aversions/what-have-you, but the more I rewatch, the more I'm realizing I don't think the main conflict was ever about Sheldon learning he needs people, or learning to like having people in his life, I think he probably always would have wanted and liked having close relationships (it is a pretty basic human desire after all), but I think he had kept people at arm's length because he had been hurt so much as a young child he no longer trusted people.
He was hurt at home (where everyone should feel safest) by his father and his siblings, hurt by neighbors, picked on by kids at school, discouraged by teachers, 'targeted' by the federal government just for trying to give his neighborhood free power, etc. The only good memories he seems to have from his formative years are of Meemaw and Pop-Pop (and trusting them got him hurt when Pop-Pop died, which also led to him getting let down by Santa) and Mary (god bless that woman!)
If that's the case, that makes any instance of him opening up and trusting people with his feelings, fears, innermost thoughts, challenges, etc. really meaningful. Seeing him let Amy into something he's always kept hidden makes me happy.