The Index Manager process does not need to be running for indexing to work. The actual indexing work is done in a background process called flpidx.exe
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The process priority for the indexing process is determined by the Threads/Priority Settings.
Note: Since the indexing process requires security privileges to read the user's local or network files the indexing is, by default, only run when the user is logged on. If you need to run the indexing outside of an interactive user session please use Task Scheduler:
How do I schedule a task to update indexes?