Hi Nitin,
No, it is not the case that a log gets generated only once there is an auth. error on BI. Once you add a user in Authorization log table, the system keeps recording the trace for every query that particular user executes. Hence, it is advisable to remove the user from that Auth. log table once you complete capturing the required trace.
Coming to capturing and analysing the BI trace, you can find good amount of information on SAP Note 1234567.
Let me know in case this still ain't answering your question.
Regards,
Pranaam