I own anice cream shop, so ive had my share of freezer issues the last, well, close to 20 years. If you can do it, no gfci. But if you have to, or even if you dont, get something like an accu rite. Even better, a commercial model from tempalert. The new ones have wifi, and will text or email you. Mine are the old hardwired style, hooked to my alarm system. You only lose 15 grand of product once before you get freezer insurance and temp sensors.
Also, commercial stand up freezers are the best. Expensive new, but so many restaurants close o go belly up, you can usually find one fairly reasonable. True or kelvinator. Reason being, they actually have a condensor you can see, and get too, and clean. Most consumer models you can't. And they have replaceable, repairable defrost timers. I've never seen one pop a gfci, but a dirty conenser will shut a compressor off from the high side switch, or throw a breaker, or both. Also,stand ups, for the most part, freeze more uniformly, and its easier to actually see what you have without digging around.
My .02 !