This is roughly correct. There are utilities that move email between IMAP folders based on their notmuch tags, but obviously the two are different concepts so t

This is roughly correct. There are utilities that move email between IMAP folders based on their notmuch tags, but obviously the two are different concepts so there's not a 1:1 mapping. The way I, and some others I know, deal with this is to simply think of their notmuch database as separate from, but complementary to, the IMAP data. The database is stored centrally. (I personally do this by replacing the notmuch command on my clients with a shell script that runs notmuch over ssh. Works fairly transparently.)