mongodb running single instance with --auth flag enabled is it means mongob running autorization enabled? I am actually upgrading 2.2.0 single instance of MongoDB to 3.2 current version.

My MongoDB single instance running with --auth flag enabled so while upgrading from 2.4 to 2.6, do I need to consider authentication and authorization specific instructions given in upgrade notes or can I just simply follow Upgrade Standalone MongoDB Instance to MongoDB instructions just copying the 2.6 binaries?
You should definitely follow the authentication schema upgrades and other procedures as documented in the relevant version upgrade instructions. The documented procedures are the only supported (and tested) upgrade path.

Upgrade steps for authentication schema changes are particularly essential, but skipping any required steps or versions on the upgrade path is very likely to cause issues with your deployment.

You should also take a backup before each major version upgrade. If something goes awry in your upgrade process or some required steps have been skipped, you will then have the option of restoring a previous known-good deployment.