That is a difficult question to answer. I know that I can live without money if the need arises and have lived without money for about 6 months. I have also lived for an extended period of time with a limited income of about 250.00 per week all inclusive for a family of five that also owns a car and had to pay rent. I guess the question should be more specific in the choice behind no money.
Not so long ago one could live without money simply by homesteading. If there were truly opportunities like that I would say yes I would live without money. If it were because I lost everything and had no family, resourses or income in the current economy as it is, no I would prefer to live with money than without. I have seen the reality of living without money in the state of West Virginia (where I reside). Some are homeless living by the river banks, some are people who have property, but nothing else. Living off the land and scraping by any way they can. Some are fortunate to have free gas due to mineral rights and use gas lighting as well as appliances.
I am too much a creature of comfort to wash my clothing in a wash tub on Monday and bake bread on Tuesday etc. unless I was in a situation such as homesteading to earn my own property and I would want all my children and my husband with me for that. When I was younger, around 18-20 years old that would have been the ideal existance as long as I could have a creek, lake, pond or ocean to bath in. (note the picture of myself, much younger that is from camping) but now, much older, my likes and focus have changed.
At this stage in my life I would have to say no, I would not want to live without money. I am sure I can survive even on Social Security (if that is still around) I would do it if I had to not because I wanted to.