For the purposes of practicality, you’re probably safe so long as you don’t have to log in using credentials tied to you. They simply aren’t going to care enough, and will likely just put up some network restrictions if they get a letter from the isp.

But for the purposes of security, yes, you can absolutely be identified. For one, if your device Mac address isn’t spoofed, they can just see what device you used, and skim security footage for someone using it in the right time frame. Even without that, they can just see who was there for the amount of time you were connected, and find you that way. Especially if you do anything that would identify yourself while there (like use a library card).