We have no evidence of that happening. Also Google themselves are on record saying that they don't use GA data for their search algorithm. I wrote a post on this topic: https://plausible.io/blog/google-analytics-seo

(I'm the Plausible co-founder)

In theory, that shouldn't happen. The gist being, Google wants to make you (the person searching) happy. So much so, it wants to personalize its suggestions. That is, if you knew what Google knows, what would you recommend to you? :) The algorithm wants to be human. It wants to be you.

In fact, in that context, if you're a pro-privacy person then Google should - again in theory - be more prone to recommend privacy-respecting sites to you. True, that's counterintuitive given Google's biz model. However, that biz model breaks down even faster when people stop returning because they are unhappy w/ search results.

Put another way, it's only a matter of time before DDG and the like use the pro-privacy signal to move sites up the SERP. DDG already knows you probably prefer that, as that's why you use DDG. It certainly would be a helpful icon DDG could add to their SERPs.