I don't know the answer. I don't think this will work.
As I understand it, the client sends to the DHCP server DHCP option 81 informing the DHCP server of its FQDN. If the MX is the DHCP server, it is not likely to use this option from the client, and even if it did receive the option there is no way to tell it to pass it onto a third-party DNS server.
DHCP 81 does not appear to be something that the DHCP server sends to the client. It is the opposite way around.