yes it can do what you want. FOG stores all of its data in an easy to read database. We looked at automating FOG from another of our applications in the past (but didn’t bother going forward as it didn’t actually save us much admin). For FOG tasks (scheduled, instant, delayed etc), simply insert something into the fog.scheduledTasks database for a scheduled task etc (the fog.taskTypes gives you an indication of what you can do). The backup process kicks in from the pxe by default in FOG. You can set a task to reboot the PC too in FOG if you wish.
Obviously it is a DISK BACKUP not an incremental backup. Expect the backups to take many minutes if you run high compression. Even low compression is a heavy task.
It will be a network backup, local backups (to USB etc) will not be possible unless you configure multiple storage nodes per PC (not practical).