You want to add the method for LISTEN to the implementation of the driver.Conn interface (if I read you right).
But then there's still the problem that it's impossible to get the driver.Conn implementation.
There is no sql.Conn because sql.DB is a connection pool. So you'd have to get driver.Conn from sql.Stmt (or maybe from sql.DB with a function).
In there, it's wrapped and unexported. This function can't be used by anything but a driver because it uses the driver's unexported fields.
Do you really want to add an exported field or function to sql.Stmt to get this?
I think this would be weird, driver specific stuff belongs in the driver package and should not confuse users of database/sql who can't do anything with it.