Mostly not. Social media platforms usually don't give out such notifications when you screenshot a photo. They respect the user's privacy to some extent. So, you can generally screenshot without the owner of the photo knowing.
On most social media platforms, a person cannot tell if you screenshot their photo. The platforms are designed to protect the privacy of the viewers as well as the posters. While they do have measures to protect against things like unauthorized sharing or misuse of content, screenshotting for personal use is usually not something that is tracked or reported to the photo owner. For instance, Facebook, Twitter, and Pinterest all operate in this way. This allows users to freely interact with the content they see, within the boundaries of the platform's terms of use.