in theory yes if it's sent to only inbox relays you control, but not sure how common that will be. in practice probably not.
Discussion
We have to make it common. Otherwise there is no point in Nostr.
I don’t see how you can make this common. People will centralize around large inbox relays. This always happens.
Unless the inbox relay is the phone/desktop node itself over tor or something, and clients opportunistically keep retrying the send, but that would be unreliable.
Make deploying a DM inbox server as easy as creating a new spreadsheet on Google.
I completely agree with your point of view, but popularizing it among ordinary people who are not professionals requires simple and easy-to-understand language.