I think people often mix up the situations of "no service" with "can't get through" when repeating this often used mantra about SMS. If your handset is not getting any signal at all, then obviously, even SMS won't work. It's possible that you may get brief, intermittent reception, in which case, you might have some success. Recall that in the James Kim family tragedy, their phone did briefly hit some cell towers intermittently.

In contrast, I have gotten SMS to go through in a couple cases where I couldn't make a voice call due to network congestion. SMS started in places like Europe, which use GSM. GSM has a separate radio channel for actual calls versus another channel for administrative tasks, like sending a signal to your phone that you have a voicemail message waiting. SMS utilizes that second channel, so even if all the voice channels are overloaded with users, SMS usually gets through on that second channel.

I don't believe other protocols, like CDMA, CDMA2000, etc., operate the same way regarding sending SMS on a separate channel, although they may have other reasons for being fairly reliable when sending SMS on a congested network. If anyone knows how other protocols handle SMS, I'd be interested to know.