The answer is yes and no, but it will only work if there is trust between you and your child. On their 13th birthday, the child will receive a notification from Google that they can disconnect Google Family Link. As a parent, you will get a notification that your child is no longer under supervision, and you can’t change the setting to keep the app running.
Using an app like Qustodio is a much better option for kids of all ages. It has all the features that you need to make sure your child isn’t getting in trouble or being cyberbullied. Best of all, the app can’t be removed without parental permission. Qustodio has a 30-day free trial that you can take advantage of if you’re not satisfied with the monitoring features.