At the moment yes this is something you would need our support for because there will be some orphaned metadata to remove from the database. You will then need to add the new server, create the websites again and restore manually from backup.
The "server disaster recovery" feature in our Roadmap will make this much smoother. You will be able to bring online a new server and automatically restore all the missing sites to this server from the Enhance backups, with all DNS being automatically updated.