Can I back up to a Shared Family ICloud account?

If you are sharing a family iCloud storage plan, your iCloud storage is still under your Apple ID, but the billing is for a shared plan. You still access iCloud storage the same way as you would if you did not have a shared plan and still do iCloud Backups the same as if it was not a shared plan. More information in: Share an iCloud storage plan with your family - Apple Support