Yes, a private Twitter account can be tagged in public tweets, but their username will not become a clickable link for non-followers. If you tag a private account in a public tweet, only their approved followers will be able to see the mention in their notifications.

For example, if you write a tweet saying, “Great insights from @PrivateUser!” and the mentioned account is private, non-followers will see the text but won’t be able to click on the username to view their profile or tweets. The private user will get a notification, but their response (if any) will remain hidden from the public.

If a private user replies to a public mention, their reply will only be visible to their followers. To outsiders, the conversation will look incomplete because the private tweets will not be displayed.

To better understand how private Twitter accounts work, you can read private tweets.