Archived from registration dashboard
No. Archiving is irreversible and cannot be undone if you used the 'archiving' feature on the registration dashboard. You will have to contact the parent and ask them to re-submit the forms.
You can add the child in the children's register and then head to the registration dashboard to unlock the form for editing.
What if the form was automatically archived when a child was 'deactivated'?
Simply activate the deactivated record from 'Centre Settings' and the registration form and all associated billing/booking records will be unarchived automatically.