Add query executed user information to Mysql binlog
Not sure about general log, but this behavior belongs to auditing system.  If you don't insist to write into binlog, both Oracle and Percona offer solutions:


https://dev.mysql.com/doc/refman/5.6/en/audit-log.html
https://www.percona.com/doc/percona-server/5.6/management/audit_log_plugin.html