An experiment is easy to run. Obtain a Kill-a-Watt or other power meter, then measure (a) how much power the freezer uses over a day w/o freezing extra ice for fan-ice cooling, repeating several times; (b) how much power the freezer uses over a day with freezing extra ice for fan-ice cooling, repeating several times; (c) how much power the fan uses blowing over the ice; (d) how much power an AC uses to keep the room comfortable, repeated several times; (e) [bonus] how much power an AC set to a higher temp. + a fan blowing on you uses to keep the room comfortable, repeated several times.

You can then compare (b)-(a)+(c) vs. (d) or (e).

Ideally, you'd do these experiments in identical conditions (temp., sunlight, wind, humidity, etc.), of course.