Also, looks like there are no issues when connecting with gnutls-cli, at least I get 

* OK [CAPABILITY IMAP4rev1 LITERAL+ SASL-IR LOGIN-REFERRALS ID ENABLE IDLE AUTH=PLAIN AUTH=LOGIN AUTH=DIGEST-MD5 AUTH=CRAM-MD5] Dovecot ready.

> Is this a publicly available server we can test?
> Can the server log things in more detail?

This is my own dovecot server on localhost. I can add test logins, if
necessary, but looks like it hangs before authentication phase. There
are no any interesting messages at serverside at first look.

Only thing I get when 'C-g' gnus is:
dovecot: imap-login: Disconnected (no auth attempts in 40 secs): user=<>, rip=..., lip=..., TLS: Disconnected, session=<HpUWrDXo+QCsEADS>