Hi Don,
No, this is currently not supported. When using LDAP/Active Directory it expects all users to have LDAP/Active Directory accounts and it disables registration because it can't add user to LDAP or Active Directory. When a user authenticates via LDAP it automatically creates a corresponding mojoportal user if one does not already exist.
It seems doable to make this possible but it hasn't come up much. Seems like anyone could register in that case, not just parents, might cause more confusion as students could also register or login that way and not be connected to their student accounts.
What would be the purpose of parent's signing in? What could they see that they could not see if they were unauthenticated and how would you verify they really are the parents before giving them access to information about the student?
Best,
Joe