Domain Controllers don't pay attention to the 'do not register IP in dns settings' (it's to do with the NETLOGON process). This means that you will get duplicate IP addresses for AD in DNS.
The knock on effect of this is that when a client requests an IP address for AD etc, the DNS servers could well respond with the backup network IP addresses which of course will mean that your workstations/application servers etc will fail because they can't see AD.
Your idea to backup your servers over a separate network is a good one - just don't include you AD servers in the plan or you will spend hours/days/weeks chasing intermittent problems with AD authentication failures, GPO processing, login time outs etc.
