Yes, in a well-designed system and this is the essence of age assurance. Age is not identity, and the check is built on separation: the website that needs the check does not perform it, and the independent provider that performs it returns only a yes or no answer, such as “over 18: yes”. The website never sees your name, document or date of birth. Where a “double-blind” approach is offered, then the provider does not learn what you go on to do.
Adults can continue to browse, read and speak anonymously after an age check, just as showing ID at a nightclub door does not mean the bartender records every drink you order against your name. Methods such as facial estimation and verification methods processed entirely on a user’s device (e.g. their smartphone or computer) neither capture nor share a user’s name at any stage.