I haven't explored that but you will run to the following problems:
1- You need to have access to the MySQL installation and be able to increase/decrease logging and restart the service
2- The way UBBT is programmed is that only one user accesses the database and in the database other "virtual" users exist to access the board. If you introduce logging in the database then you will only get the user that connects to the database and not the users that log into the forum.