A Domain Controller is not a stateless server; quite the opposite: it hosts the Active Directory database, where everything about the domain is stored, including authentication for users and computers. Also, this database is replicated between all DCs in the domain, and they send updates each other and employ several solutions to ensure ...
This is not a good idea. You need to have multiple domain controllers, but they need to be online and communicating with each other. It's also not a disaster recovery plan.
And no it may not work for a variety of reasons.