COBOL Indexing is the scanning of programs for dependency information (i.e. copy file usage), without up-to-date index information changes to copy files won't cause the programs which use the copy files to be rebuilt during an incremental project build.
In V2.2 this same COBOL index data is also used as the source of the information when showing the copy file dependency information in the COBOL Explorer and Copybook Dependency views.
There was a very significant change for V2.2 in that the COBOL index information is now obtained from information generated by the last build. The background indexer is still used if you add files to a project and you have "Directives Determination" turned on the preferences, but otherwise it is skipped. This can mean the COBOL index information is out of date until after a build has been performed (this is planned to be addressed in a later version).
With the indexer turned off you will have no copy file usage information and incremental project builds may not build everything they should but it would have no impact of single program compiles.
For V2.2 unless Directives Determination is turned on (and you add files to the project) I don't think you should be impacted by the indexer as you were with 2.1 - if it does run you should be ok to just cancel the job (although this will mean the directives determination doesn't execute).
I don't believe the indexer has ever had any impact on debugging local or remote as the information about which files to show during debugging comes from the .idy files created by the build.