It is not about a "database" but about a table that sotres users data. When I use phpBB Component I have only one place where users data is stored. In the solution with "regular" phpBB - I have two tables within one database that have redundant info. For me this approach is not good because it can lead to inconsistency between these tables.
Buy once again - my errors are probably not directly related to phpBB component...
you are correct that the specific error message you are seeing is not directly related to the phpBB component. That error is indicating that you have not correctly set the "forum directory" in the plugin parameters (notice it is looking for the users table instead of phpbb_users... missing the prefix)... this means that it is not loading the common.php (and other) files from phpBB and therefore does not know the table prefix.
By fixing the forum directory you can get rid of that error but unless you have hacked the plugin it still will not work completely with the phpBB component because it uses the 1 jos_users table where as the plugin registers users in the phpbb_users table... this will cause users to not get registered correctly and it may not start or end a session correctly.