Hello,
In fact, it won't work as described.
When user is synchronized manually, say, from Joomla! to forum, an "incomplete" user is created in forum, i.e. his name, e-mail and other data is copied, except the password. Hence, the password field remains empty which prevents user from logging in directly.
When this user logs in in Joomla! the password becomes updated in forum. Only then will user be able to log in in forum directly.
If, for some reason, user passwords will differ in Joomla! and forum, the autologin won't work correctly.