CDMA and AMPS/D-AMPS may or may not work, depending upon range/power
issues. There are no technical barriers.

CDMA allows for multiple towers to be in simultaneous contact with the
Mobile,so that isn't a problem.. However the speed of the aircraft
might make the fast Rayleigh fading occur at a higher rate than the
power loop can deal with, so it may not be especially reliable.

GSM is more troublesome because of something called timing advance.
GSM signals must arrive at the tower within a specific time frame.  To
do this, the tower commands timing changing in the transmissions from
the phone. This is only good for up to 35km from the tower.
If you are crusing at say 35,000 feet, you have already consumed about
10 of 35km range limit, and in fact, at best you will remain in range
of a ground cell for 2-3 minutes.  If the tower is more than 18 miles
from the center line of aircraft's route, you will NEVER  be within
range of the tower. You can hear it, it will display on your phone,
but you will never be able to make or receive a call because you won't
be able to register on the network.

This also makes it not all that likely that your phone will attempt to
talk to more than one GSM tower at a time, not that a .125 watt RMS
output will work all that well over a 35km  range....

So the answer is that unless you happen to be over a relatively
populated area, GSM mobile from a commercial aircraft won't work very
well.

The obvious exception is where the aircraft itself is a pico-cell, and
is effectively the bts. This  capability has been demonstrated  on
aircraft for both CDMA and GSM systems.