I think society is rapidly moving away from paper and coin currency in recent years, I think it will just gradually be phased out in the next decade, nearly everyone used a debit or credit card at the stores now and there are very few places where cash is necessary to keep on you.
yes, i do think that there is a way that the society can function without paper and coin money, and there have been a lot of tiimes in the history of places where this has been the case. I think though that a lot of people would not make it.
I think it is possible for society to function without the use of paper and coin currency. Most of the people I know, including myself, do not really use paper or coin currencies anymore. Plus I think it creates a more efficient system when everything is paid for using something like a debit card.
There is an element of worry that should be at play in a society that is fully digitized, and that is who is running these servers, where is this money, what is this currency? There must be some sort of value that is natural and not completely digitized or artificial.
People still use paper left and right. Coins on the other hand could be eliminated. Paper currency could be eliminated. Really all you need is an ATM/debit card these days. Some people I know never carry cash on them. They just use credit cards and their ATM card. I think many people still like cold hard cash over the modern technology stuff though.