Immortal auto-deletions don't show up on the Battlefield because occasionally someone will auto "by accident" and want to (usually immediately) come back and so everyone saying their goodbyes is kind of weird.

The distinction is that sufficiently high level immortals never auto-delete.

In this case, considering Aarn auto'd within a few months of returning it would surprise me if we see him back on the wizlist any time soon.

EDIT: And like Dest said, any time an immortal (of any level) deletes themselves they go to the Battlefield like normal.