Situation: IMAP mail account A accessed from distinct clients X and Y. X reads a message, is it marked as read for Y? Also, assume message M is marked as read for X and Y, and X marks it "Unread". Is that sync'd to Y?
Yep, IMAP should do that. It'll sync as long as the clients are accessing the same mailbox.
https://support.google.com/mail/bin/static.py?hl=en&ts=1668960&page=ts.cs