If the question is narrowly and concisely interpreted to mean "can an economy function with an electronic-based crypto-currency in the absence of government/large organization-backed-exchange medium" the response is an unqualified NO (thus obviating the sub-questions about market distortions and market implosion).
A. Human (above, I don't possess enough reputation to comment) also says "no" at the outset, but then charitably recasts the question to mean 'can an economy function with an electronic-based crypto-currency backed by the user's government/large organization currency of choice' and answers 'yes'.
Keith S. answers 'yes' to the original question without any modification.
I answer 'no' for two reasons
- No medium of exchange has value unless it can prevent, mitigate, or reduce coercion and/or violence.
- Mediums of exchange have little practical value (only possessing speculative value) unless people can agree, within a relatively narrow range, the present value of the medium relative to some other good/service/value - and is why these are known as 'mediums of exchange'.
Bitcoin possesses practical value in relation to current currency (USD, JPY, EUR) due mostly to its speculative value, and to some degree to Bitcoin's intrinsic properties (anonymous yet transparent transactions, known current and future pool size, suicidal disincentive to subvert the bookkeeping).
Without some confidence that bitcoin can be and will be exchanged for government-backed currency, or similarly-valued goods or services, bitcoin possesses less value than its cost of generation (electricity and hardware).
Bitcoin gets exchanged for currency, which is exchanged for goods and services.
Bitcoin has negative value otherwise (as it costs electricity and hardware to generate bitcoins and maintain records of their transactions).
I do agree that currency itself possesses no intrinsic value, but its issuers have a stake in maintaining its current value.
It is true that no currency or commodity (gold, silver, gems, iron etc.) possesses intrinsic value BUT government-backed currency DOES maintain (above all else) one specific value: Taxes are assessed in terms of (local) currency and payable with that currency. Without governments/large organizations to levy taxes, and in absence of other mediums of exchange, one would be relegated to a barter system, a form of economy with very low potential for growth as there is ultra-low liquidity and almost no opportunity for investment and credit.
Could a future crypto-currency, with 'government' backing, yield a useful economic system, in the absence of currency? Sure!
Since the mid 1960's there's been increasing discussion of a world economy with so much surplus that there is an 'end to scarcity'. All basic material needs are met, globally. Creative work abounds, and I'll trade my garden-grown strawberries for you painting my shed.
The underpinning of post-scarcity economies is that for the work that needs to be done, that no one wants to do, is performed (generally) by the young and middle-aged, and work is a form of taxation. Do nothing and you'll get a dormitory bunk, 'welfare gruel', shared internet access on a public terminal and basic clothing. Labor a month a year harvesting lettuce, digging ditches, providing hospice care etc. from 20-40 entitles you to some luxuries. Being the farmer, civil engineer or nurse for 10 years out of your life will earn you much more. Obviously there is incentive pay for difficult/dirty/long-duration/dangerous/skilled-professional work, and jobs well done, and penalties for slacking.
Want life extension? Work like hell for d decades
Want a permit to have a family? Work like hell for y years.
A free market for labor needed and goods/services desired could be managed (ideally) with a crypto-currency, but would still require a government to be able to coerce those who would not honor contracts, to prevent or punish theft, vandalism or violence, and, ultimately, to intervene during emergencies (famines, disasters, plagues etc.) and of course, to regulate the market and transactions.
Libertarian Anarchists/Capitalists would disagree with the 'government' part, but a group of people, legitimate, with the power to coerce, is a government by any other name.
So, if you're looking for a world with a secure, functional economy, transacted through a distributed crypto-currency without tangible paper notes or coinage, use labor value theory as your 'cashless as possible' alternative.
Finally, if your universe REQUIRES the lack of government/large organizations, to be cash-and-coinage-free, and necessitates a crypto-currency (sigh) I suppose you link crypto-currency to a reputation-based barter system.
As the recent de-nationalization of state-property in post-Soviet-Eastern-bloc-countries has demonstrated, you can give people titles to their flats, shares in the companies/farms/oil fields and mines where they worked and in a few years they were about as poor as they were under 'communism'.
In other words "After the aliens left and wealth was evenly distributed ..." if everyone got 1/th share of the world's wealth, in a short period of time, that wealth would be concentrated (again) in the hands of relatively few people.