This is a difficult question in that it is very difficult to prove that something is impossible. However, based on the types of analysis done in financial markets, estimating supply and demand curves is obviously difficult to do.
The usual methods for valuing assets in financial markets is to rely on some relative value versus a similar asset, or discounted cash flow. For a currency, we can compare the prices of similar items (hourly wages, goods prices) to get fair value. However, I am unaware of items sold at fixed prices in crypto currencies that would allow us to use a similar valuation method.
As for supply and demand, unless we have a reason to know that supply and demand curves follow some particular parameterisation, all that it says that for every buyer there is a seller. A price change can either be explained by the supply curve or the demand curve shifting (or both); we have no idea what happened. There is no clear method to go from observed transaction data to back out supply and demand curves.
For example, imagine there are a sequence of transactions at rising prices. Is that because there was an increased demand by buyers, or was it the result of existing owners being less willing to sell? Since every transaction has two sides, we have no idea. All we know for sure is that the price went up - which we could see by just looking at the time series of prices.
Furthermore, prices can change without any transactions. In the financial markets, prices jump on the release of economic or corporate news. This is much more easily interpreted as a change in fair value, rather than a shift in demand or supply curves.
Finally, it is unclear what a supply or demand curve represents. In the short term, a crypto currency supply is fixed (at least until the next coin is “mined”). How exactly can the quantity supplied or demanded change?
In other words, probably the only way to see whether “supply and demand” work is to build a model that works. I am unaware of any successful attempts in other asset markets to build such a model, so you have little guidance on how it could be done.
Addendum: It is difficult to control supply to keep an asset near a target level. Preventing the price from going up is easy, as you could just flood the market. Stopping the price from falling is difficult. You cannot destroy currency units held by people, and so you cannot reduce the amount outstanding. If people want to sell at a lower price, there is little you can do except buy the crypto up with some kind of currency reserves. (Which is how currency pegs are defended.) However, currency pegs tend to fail. (I believe some crypto currencies follow a backing strategy; I do not know how popular those currencies are are.)
