Yes, I've run low dose (250mg/day) DNP on a low carb diet. You are flat as all get out with no carbs and the DNP depleting every last bit of glycogen, but you don't need the carbs.
Low carbs, IMO, make the DNP sides less drastic, as I tend to feel hot and sweat more when I've ingested carbs. If I were to eat a large piece of b-day cake or eat a large bowl of ice cream, I would start sweating profusely.
I think of DNP as a compound that makes your energy conversion machine less efficient, with the reduced efficiency lost as heat. Thus your body has to work harder to use the fuel you ingest, thus making your body have to tap your fat reserves.