Is there an event in Joomla that one can use to catch/modify Joomla queries sql in a system plugin?
If this is not possible can we override Joomla database class? so we can add the desired event?
No unfortunately no.
This is the list of events you can have in a plugin : https://docs.joomla.org/Plugin/Events .
About the override on Joomla database, well yes you can of course. It's just a php file like the others. Just be careful with the security and when you run the updates.