No. Kind 10002 is only public outbox/write relays and public inbox (that is for things like replies and reactions to public posts).

I would not want someone sending a DM to my wot.brightbolt.net, for instance, or relay.brightbolt.net/inbox. Rather, I only want DMs to be sent to inbox.nostr.wine and relay.brightbolt.net/chat, hence why they are a separate list.

10002, as far as I know, has no means of differentiating between which relays are public inboxes and which are a DM inboxes.