The server configuration creates two tables in The Raiser's Edge database; one to store the audit and one as a table that creates transaction sequence Ids.
The config creates a SQL Server user so that Audit Trail Classic can write to two tables that it creates.
The config sets up the user so that it has rights to write to those two tables and read from a number of other RE tables such as the RECORDS and the LOGINAUDIT table.
Once it has done that it writes the connection string for the SQL server user that it created back to an area of the database that is accessible via the API. It does this via the API so that Audit Trail is able to pick up the connection string (again via the API) and then write changes to the Audit Table. This is the reason that you are required to log into RE via the config application.
At no time does any Audit Trail Classic component write directly or run a stored procedure that writes directly to a Blackbaud created table.