The failover will be handled automatically by ISE, but you must have at least one of the name servers available (specified with ip name-server x.x.x.x from ISE cli)
As long as there is at least one other DC available for ISE to join to when the old ones are switched off, you should be fine.
The success of this operation depends on the health of your AD (SRV records, etc). One way to check is to run the AD diagnostics tool from ISE.
Best to do this during off-peak hours or maintenance window of course...