No doubt an AC unit will work. I've seen too many examples of that. There is also the coolbot controller that really works well and keeps them from freezing. It still won't work in my closet under the stairs. The basement is finished space except this little storage closet and I can't point the rear of an AC unit into my basement hallway or my office. The exhaust and condensation have to go somewhere. I live in a golf community and an AC uint sticking out the window is just begging for HOA sanctions
So I have abandoned that plan.
Plan B: I'm buying a 10 cu ft fridge at Home Depot. At $400, that is cheaper than buying an AC unit, insulation, vapor barrier and something to cover up the barrier and insulation inside the unfinished closet.