possible? For sure. One assumes the Gulf of Mexico? Getting out of the gulf will be a good test, as there are quite a few obstacles (drill platforms, oil wells, abandoned/etc) and a fair amount of traffic. You can bounce around the coast and not be more than a day away from a port, if you need a rest or find that you can not adjust to a full time watch with naps.
All depends on your skill and how the boat is set up. Size and type are a bit down the list, as single handling and being competent at it usually begins in small boats and grows from there. Skill building will show your weak points and what the boat needs to work with you. Most would want an autopilot and a radar so you could nap a few minutes at a time and still be able to respond to traffic or weather changes.
I was quite comfortable with single handling my Sabre 38, but when I moved up to a Passage 42 Center Cockpit, it was tougher to single hand and the boat responded completely different than the Sabre 38. The hardest part for me, single handling was bathroom, sleep, and food (real food - not garbage) prep in that order.