On OS X, does Time Machine need the index maintained by Spotlight? Will disabling Spotlight completely (via
mdutil) affect Time Machine?
Yes Time Machine require a spotlight index on the backup volume. As a result, you cannot add a Time machine volume in the privacy list.
Apple explained this by stating:
If you add a Time Machine backup disk to the privacy list, you will continue to see messages that Spotlight is indexing your backup disk. This indexing is necessary for Time Machine to function properly and can’t be disabled. Spotlight does exclude from searches any items you store on your backup disk that are not part of a Time Machine backup.
I have just tried adding my TM backup drive to the exclusion list in Catalina 10.15.4 and it was refused stating that I cannot add a Timemachine Backup to the privacy list of spotlight. - Others have tried the same in Mojave 10.14.2, in Sierra and High Sierra, with the same result.
Again others have tried doing this more ingeniously in the command line, only to find that mdworker continued to access the backups making indexes.
Oddly, though, Apple has removed its earlier article(s) about this altogether, and there is no longer any official line as to whether it’s possible.