The "dehumidification" capabilities of a standard a/c unit are dependent on ambient temperature and dewpoint. They do not always remove moisture from the air. But, regardless, a properly-vented wall fan will remove significantly more moisture at less expense.
If the cellar is already at the required temperature, the air-conditioner unit (I presume we are talking about a window/wall unit) will be running on fan-only. There will be no condensation on the evaporator fins or coils, and thus there will be no dehumidification. The a/c unit _may_ help in the summer, but not in the winter.
You can get a 5000 btu a/c unit at Home Depot or Walmart for less than $100. But it is the cost of operation that is significant.
The a/c unit will give off considerable heat (in back), and any condensation (that is not recirculated by the fan) dripping will tend to humidify the cellar room next door, which will find it's way back into the room you are cooling/dehumidifying. Some form of venting system would be advisable.
I guess none of the a/c's sold around here are "properly-designed", because they will NOT go below 65°F in the summer time without frosting up. They don't seem to have adjustable defrost cycles. Of course, now that it is 40ºF outside, the a/c has managed to reduce the temperature to 62ºF, but a partially open window would do better.