Yes and yes. Whenever a DMCA takedown notice is filed with Google the allegedly infringing URL is quickly removed from the SERP. Google will notify you (and the public) in following ways:
1. Publishing the request on lumendatabase.org
2. Informing you through the Search Console (which has a delay of a few days)
3. Publishing the removal on Google Transparency Report website
4. Publishing a note at the bottom of the SERP mentioning that a website was not featured on the results due to a DMCA takedown notice with a link to lumendatabase
Google takes the ”I trust you bro” stance and delists your URL until (if ever) you file a DMCA counter notification which can be done through Google (can look up the link if you need it).
I don't necessarily think it's "I trust you bro", I think it's more "Section 230 requires us to delist any content immediately until a counter claim is filed to maintain safe harbor protections".
But I'm not a lawyer. Just listened and read a lot about this kind of content.
