de0u Second experiment: I turned my phone off, sent an SMS, waited two minutes, turned my phone on, waited for it to boot, waited another minute... and, before I unlocked, there was a notification: "You have new messages. Open SMS app to view". When I unlocked, before I opened Messaging, the regular SMS alert popped up and the Messaging icon acquired a pink notification dot.
So it seems as if the article linked above may be correct (in my case): if the phone is off, some part of the network periodically tries to deliver a pending SMS, but the timing may be random on a time scale long enough that it's unpredictable.