Anecdotally, I've gotten curious and messed with this setting. I'm pretty confident (>80%) that I could see a difference in what ads I was served, with logging-disabled searches not influencing my Google ads they way logged searches did.

Honestly, this article felt a bit FUD to me. Google's privacy text never led me to believe they would purge all record of no-log searches, just that they wouldn't attach them to my primary profile. As far as I can tell that's still what they're doing.