Recent findings discussed at WorldCALL suggest that many students like to use their smartphone as a device to be updated on their status in a course in preference to logging in to the LMS and seeing the same kind of report within that interface. This is true even of the majority of students that prefer to use the LMS interface on a laptop (or iPad-size device) to do the actual course work in preference to the device they use for monitoring messages and updates.
Wrote to Erik and Mark regarding degree of support within UVic moodle instance for that kind of thing. They report Moodle does not have the capability to relay messages directly through an SMS service, but most mobile carriers offer email-to-sms, so if Moodle knows the sms account (e.g. 2501234567@txt.bell.ca) it can email out and have the vendor render the email as a text message. Obviously that would have to be tested to see how it performs with real data.
Second issue they raise is that Moodle does not have strong features to support sending out automated messages, let alone with updated user-specific information the automated message. That sounds like a more serious problem. In principle all the necessary information is probably in Moodle, but it would be some kind of plugin that could extract the relevant bits and compose a useful report to the student.
I'll follow up with them and see if there's any more detail they can provide.