Looking at it the other way, why don't search and rescue services have a mobile cell-phone "tower" attached to an aircraft?
Movement is not the only thing that can cause a Doppler shift, echos, and multi-path propagation are also a pain to deal with but for the movement part phones pretty damn early started having accelerometers (way before they were used for cool stuff) in them as well as much better Doppler estimation processing at both the towers and in your phone.
At 150knots (relative speed, this will depend on the altitude and heading of the aircraft in relation to the cellphone) a 1.9ghz signal will have a Doppler shift of about 500hz which is more than enough to induce blocking of pretty much any cell network. Radiophones that allow air to ground communication to exist but they are designed for this purpose and implement quite aggressive Doppler correction which is also usually only possible when they have the flight data and they know more or less the altitude, heading, and speed of the aircraft based on the flight plan and real time flight data and can adjust the Doppler correction in real time, as without it it won't work.
P.S. Blimps would probably work.
Capturing signals and reconstructing them isn't hard when you fly special mission aircraft.
But you can't just strap a picocell to a SAR aircraft and expect it to work.
Also cellphones don't have that much of a battery life if a hicker has one its most likely going to be either off due to them being out of coverage or dead due to battery drain by the time anyone figures out they are missing.
Considering the cost of such platform and the little to no use it will bring the money is probably better invested in high resolution FLIR cameras and more aircraft since anything that could ping a phone and get its location would cost more than a civilian SAR aircraft.
Does a similar thing happen in the US?
Also seems like a perfect application for those Stingrays the police have stockpiled.
http://s9.postimg.org/umb1a3tjz/s5570.jpg
Besides 911 there are probably a few other emergency numbers in the US which are open on all cellphones, as well as the emergency broadcast system which will display push notifications on every modern cellphone in such cases as natural disasters.
LTE, however, is making this less of an issue and in theory an LTE capable phone should be able to make an emergency call from any network.
Government surveillance already has multi-band and protocol mobile tower stand-ins.