When my Public Cloud service is operational again, can I choose not to reboot my server?

All Public Cloud instances will be recovered while they are powered down. You will receive an email communication beforehand, so that you can decide in advance how to manage your instances.
You can then launch your backups in a standard way using the APIs, the Horizon interface, or the OVHcloud Control Panel.
For further information, please read the following guide: https://docs.ovh.com/ca/en/public-cloud/get-started-with-a-public-cloud-instance/#reboot-an-instance