Interesting idea. Probably could, but it wouldn't pass inspection for registration as quarters on a vessel itself, so you'd have to have it as cargo. Then I guess if/when declaring cargo crossing borders you'd have to say a couple of humans in this box thing, which is odd and sure to raise eyebrows, smuggle you or list you as crew. So basically you'd be paying for the barge anyway, and living in worse conditions in a largely uninsulated (and probably power hungry) box on board.

What's the point? Just get a boat. There are many cheap boats, many people live on them. Check https://www.yachtworld.com/ http://www.cruisersforum.com/ https://sailinganarchy.com/ for a start. Roughly <=USD$20K will get you something that floats and 1-2 people can live in cramped but OK.