Will a malfunctioning thermostat on a window ac cause it to freeze up?

No generally not, the thermostats only function is to close the circuit between R and W this only controls the set points required in room, it doesn't actually make the a/c unit run colder.

Remember there are only 2 basic ways to freeze a coil, first is to retard the airflow across the coil so severely that the refrigerant is unable to extract the heat from the air leaving the coil temp below freezing this allows for the build up of moisture along coils Finns causing frost to start to build up which will then block more air and compound itself to a solid block of ice. The other way a coil will freeze is if there is too little charge within cooling circuit, remember what makes something a refrigerant is that @ a given temperature it will always be at a specific pressure and inversely if you lose enough refrigerant the coil temp will drop below freezing and you will end up with same results ICE