I don't think it will. While I personally hate AMP, and disagree with many of Google's practices, this is not the solution. Google is everywhere.
It is the default search engine on almost every browser, as well as on most devices. How often do you hear someone say "look it up" as opposed to "Google it"? The latter is much more common in my experience. Google is synonymous with internet searches.
Outside of tech circles, no one is going to make an effort to even try other search engines. There's a reason Bing and Yahoo are treated as a joke.
Google is also the best at searches. While other search engines are slowly catching up, and Google's own results are becoming worse, it's still way better then most search engines - especially when it comes to specific and local/regional results.
Lastly, blocking Google means that you site also won't show up on Startpage.com results, because it sources results from Google. This is unfortunate, since Startpage is definitely one of the search engines that respect your privacy the most.