Unconvinced - sounds like you're just re-inventing log_line_prefix.
Thanks for your inputs.
I thought, it will be helpful without modifying the log_min_messages parameter. Otherwise, we have to run the vacuum verbose, by modifying the log_min_messages at session level, which will be recorded in pg_log.
If we allow VERBOSE to log timestamp, we can have it in stdout, which can be diverted to a required log file. This will be useful for the vacuumdb binary too.