Yes, if the failover is to a Server instance which is initially idle, all the items have to be subscribed to again and no snapshot information is available within the Server.
Note that the Data Adapter, upon the subscribe call, has the opportunity to send to the Server kernel the current snapshot, if you have kept it somewhere in the system.

I confirm that upon unsubscribe all snapshot information is lost by the Server kernel; as said above, the Data Adapter could restore the snapshot at the next subscribe call.
Note that unsubscription only occurs when all the clients interested in the item have gone and that, in case of page refresh, the Server tries to keep the previous subscriptions for a few seconds, so that when the new page asks for the items they are still subscribed to.
You can force important items to never be unsubscribed from by using a custom, internal client, which requests them and stays alive forever.