I don't think you can do this out-of-the-box. You will need to customize the store. Perhaps you could create a new user group in the admin and assign your customer(s) to it. Then assign hidden products to a hidden category. Your customization would need to check if the user belows to that user group, and if they do, display the category and the products. I'm just thinking out loud here, but I think this could be done without a ton of work.