Someone said the network can tell when you start to compose an SMS message. I say they can't using regular SMS and if someone thinks they can, they better be able to prove it by citing a credible source. SMS uses the old GSM protocols for cellular broadcast systems. It simply doesn't send anything until you press the send button.
Now a phone manufacturer can put additional software into the phone so that it can detect log this and send it (e.g. via the internet connection) but if they did this it would be similar to the CarrierIQ privacy scandal and it would be all over the tech news (again).
Now IM (instant messaging) is of course a different kettle of fish and you'd expect the IM service to know when you start typing. However again there's no reason the phone provider would know unless they were one and the same, and in many cases they aren't.
Thanks for clarifying that.
So, in summary:
a) there is no reference in what has been published to date (i.e. the AAIB's Special Bulletin) to anything other than regular SMS/text communication was being used
b) the network would have no knowledge of any SMS/text that had been composed by the pilot, in full or part, but not yet sent, in the period between the last text sent and the collision