No! This is not the 'scope' or the 'purpose' of SQLyog.
SQLyog is primarily a tool for DATA MANAGEMENT with MySQL. Not for management of the SERVER ENVIRONMENT. As a MySQL client it does not (by accessing server logs or by any other method) try to read or to interfere in what other clients are doing.
However SQLyog does provide tools for user management, table diagnostics, 'killing' of user threads with the MySQL server and similar things.
Basically SQLyog provides the features that you need in your daily life with MySQL once the MySQL server is installed and configured.