I know that, in terms of UI, this is not precisely the SublimeText equivalent of an email client but have you taken a look at notmuch[0]?

It basically operates on your local Maildir which you can keep in sync with your mail server by using a tool like OfflineIMAP[1].

[0] https://notmuchmail.org/

[1] http://www.offlineimap.org/