Yes, you typically don't use carb heat on take off or landing as it can effect power. It's possible they didn't use it in the first place or for long enough. It's also possible they started getting carb ice after takeoff when they reduced throttle. I heard when the engine started sputtering they signaled mayday and prepared for a forced approach landing. Being at 2,000 feet and not knowing what was wrong with the engine, they probably didn't try turning on the carb heat. Their first thought was, where are we going to land. It's not like a car, you can't just pull over to the shoulder. When something goes wrong with your engine, you have precious little time to figure out what to do. It can be a matter of life and death.