If the 2 controllers are participating in different domains, then during the failover, the taking over system won't be able to join the other domain.
And why is that?
Failed over controller exist as a virtual entity inside the other controller memory, so it still has its unique host name, separate CIFS server, different IP addresses, etc. - so IMHO it shouldn't be a problem.
Let me know if I am missing something.
Regards,
Radek