I have turned the indexing off a few months ago without any ill effects, other than the Start menu Search box results are limited to software and settings now (that's how it works when indexing is off -- we don't have settings to change that). Because I
prefer to decide where I'll search for documents at the time that I do an actual search, and I don't use Libraries, I don't mind that limitation, and I go to a folder and use the Search box in the window at the upper right corner, where searching works as
it always did. I have not noticed any unasked-for attempts to start the indexing happening on its own.
I'll mention that without indexing on, we can't manually specify new file extensions to enable Search to search the contents of, because Indexing Options is not available when indexing is off, and and that's where Search (unwisely) put those settings.