Yes, but even more specifically as it’s only for private messages. Amethyst lets you select what relays to write a DM to, for example. If both you and your recipient had inbox and only wrote DMs there (kind 4 or giftwraps) the metadata would never leak (except to the relay operator).

Inbox also lets you delete private messages where you were the recipient (like an actual email inbox) using kind 1984 reports as well as messages you’ve authored (with traditional kind 5 events).