Not completely correct, but on the right lines...
GSM and 3G phones listen to the cell tower's Pilot carrier, which contains a whole bunch of data (which network, neighbouring cells etc). thenetwork will broadcast a request for a particular phone to contact it when there is incoming traffic (eg call or SMS) for that phone.
To reduce the volume of traffic, it only broadcasts this request over a small(ish) no of cells, called a Location Area (LA). And how does it know which LA to poll - because part of the broadcast data on the pilot channel is the LA identifier - so when a phone switches from listening on one cell to listening on another (which it doesn't inform the network about unless it is mid call) it checks the LA number, and then updates the network with it's new LA when the LA identification changes.
So if anyone on the plane left their mobile switched on (and with a couple of hundred people on the plane this is a racing certainty), then by checking the operater records for all the phones, LA updates will be there (and yes, operators are required to keep this meta-data for the intelligence services).
In consequence, I would be extremely surprised if the NSA / GCHQ / KGB and Chinese Military Intelligence did not already have a good indication off where the plane was (or was not).