Yes, it is POSSIBLE. But there are some problems due to
characteristics of the cell phone system. First, you need
to know the frequency that the cell phone will use to try
to contact the base station. That depends on which carrier
they are using, where they are, etc. If the phone is
out of coverage range it will keep trying to contact the
base at high power (as would any other cell phones in
the area.) If you could separate out which signal was
the desired one, you could try tracking it. That would
require some sort of receiver that could decode information
from the signals, however, which probably would have
to come from the cell company, unless there was only one
cell phone in the search area.
Practically, if the cell phone is on and is out of a
coverage area, it won't last long. That is because it
keeps transmitting at high power trying to connect to
the network. My guess is that most phone batteries won't
last more than 12 to 24 hours in that situation.
If you can find out from the phone provider what frequency
it would be transmitting on, and if the lost people
turned it on occasionally to check for coverage, then
you would have a chance of listening for the signal if
there were no other phones around to cause confusion.
You could also contact the phone provider to see if their
phone had contacted any of their cell sites - that might
help to narrow down the search area if it had.
I spent 10 years in Search and Rescue, and get asked
by the local Sheriff's department to help with DF projects
including ELT beacons, interference to their radio systems,
etc. Other local hams are involved in Project Lifesaver,
which uses radio tags to find patients who tend to
wander away from home.