I picked the machine up this morning - absolutely spot on the money. Brand new glossy screen, all tip top. I had a quick browse through /var/log/secure.log to see when the machine had been used, and it looks like twice - once the day after (I assume to diagnose the fault), once on Thursday where it was on for a fair while (I assume after they'd installed the screen) and again yesterday just before they called me.

All in, rather impressed - Applecare seems well worth the money. Well, if you paid as little for it as I did - 30 quid for the extra 2 years.