The problem is, if you make it that thin and the cavity is mainly supposed to be used by the door, you won't be able to put any insulation in. So you automatically get a resonating body. Acoustically, that could be very unsatisfactory. Is a sliding door absolutely necessary? Maybe try it without it first? We had originally planned a door between the open space and the hallway, but didn't install it at first. And in everyday life, it actually works fine without it. A sliding door doesn't offer much soundproofing anyway.