Is it possible to perform the backup on the read-only copy of a scale-out server instead of the productive server? My idea is to spare the productive server from the effort needed to do a full backup.
Unfortunately, the answer is no. The backup must happen on the server acting as the root server (or the primary server in a mirroring system). Backups require that the server performing the backup be able to control when checkpoints occur, and this is not possible on a copy node or on the mirror server.
Is there any chance to do full backups (those big database files) at secondary sites, and only log backups at the primary site? (The answer will be no, I bet...)
Well, following Bruce's answer, as both types of backup require an internal checkpoint, there seems to be NO CHANCE to combine backups from different sites, simply since backups on secondary sites are not possible at all. (Agreed, it was a crude idea:)