It would be quite amusing if it couldn't work with AD, considering Zulip is based on Zephyr which is a very old chat protocol/application heavily dependent on Kerberos.
Just FYI, Zulip uses a similar UI model to Zephyr, but doesn't use the Zephyr protocol internally. (For example, Zephyr doesn't really work when one user is behind a NAT)
(I worked for Zulip, and have contributed to the open-source project)