Yes, because there are specific exceptions in the GDPR that allow data processing and storage in many of these cases. However, managers are pissed off by the law, or just ignorant, and they make you sign a document that has no legal value.

Heck, many documents that I saw while interacting with P.A. in my country are lacking the basics, such as "what are you doing with the data".

One clinic once made me sign a document where they said that I received a copy of the privacy policy (which was not given to me). I politely asked for the privacy policy, and they sent me the entire GDPR regulation PDF. I spent one hour explaining to them that they need to fix it.