Sure. The challenge is power for the a/c. While some folk have used really huge battery banks and quite small a/c units, the conventional approach is some form of generator. On a boat your size you could use something like a Honda EU-2000i and a small 5k or 8k BTU a/c that only cools the v-berth.
Whatever you do, be sure the generator and a/c are sized together and take into account any other loads (water heater, microwave) you might use at the same time.
sail fast and eat well, dave
beware "cut and paste" sailors.
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