Can we use customised metric to detect the web application version being used by the user?

By "web application version" I assume you mean something like the build version that your developers using in their version control... like something that you could use to trace back to changes that were deployed?

This shouldn't be a problem, you just need to work with your developers to provide the build number into a data layer that you can read from the page and track...

Or do you mean an "analytics" version number correlating to your Launch implementation? In this case, this would be something you would need to maintain... make sure you are using a "version number" on your builds, and use a "constant" Data Element that you make sure correlates to your versions... this is a little bit manual, but if you are diligent this is still doable.