Fed power limits after bitcoin (part one?)

This post was inspired by a post on "In Crypto We Trust" http://incryptowetrust.com/cryptonomics/ . Many supporters of bitcoin hope that it will someday completely replace conventional currency, and this obviously would end the economic power of central banks such as the Federal Reserve. In this post I want to look at the obstacles along that path, and what direction it might follow in the short term. Particularly, I am curious whether wide-spread use of bitcoin for transactions would inhibit the power of the central banks.
Bitcoin is an online peer-to-peer currency and payments system. It is not associated with any government, and due to its p2p architecture, no single government can shut it down.
Traditional econ describes money primarily in terms of 3 functions: medium of exchange, store of value, and unit of account. Despite various factors opposing innovation, the monetary system has been moving toward separating these functions for decades. This trend may accelerate as a result of the arrival of bitcoin. It is already difficult to say what is and isn't money, and will only become more difficult.
The rise in popularity of money market mutual fund accounts in the early 1980's illustrates the idea that we can use nearly any asset as a store of value and medium of exchange. People using these accounts can write checks against them like an ordinary checking account. But the interest earned comes from the notes and short term bonds owned by the fund, rather than an arbitrary deal with a banker. The mutual fund disintermediated the banks, allowing the share owners to increase their risks and rewards. The checks can clear in various ways. The most general approach is that it would go through the bank clearing house, like an ordinary check. But it is also possible that the MMMF could transfer securities or other assets to another fund to clear their balances. (In the case where the clearinghouse uses dollar denominated bank deposits or notes to clear checks, dollars act as the medium of exchange, but in some cases stocks or bonds may be exchanged instead, at least in principle. I'm not sure whether this happens in actual practice. I suppose it would in the rare case that I write a check to someone who then deposits it in the very same MMMF that it is drawn from, so that the check could be cleared merely by updating the balances of both our accounts.) This practice (having checks or debit cards that draw on the balance of a mutual fund rather than a conventional bank account) quickly spread to ordinary stock mutual funds and others, so that we can now use almost any financial asset as a store of value and medium of exchange. So, are all these assets "money"?
We have not discussed money's function as unit of account. This means that when I do my double entry bookkeeping, my credits, debits, assets and liabilities will all be recorded in terms of money values. (For the uninitiated, double entry bookkeeping was an essential business innovation that still provides the foundation of accounting and lets entrepreneurs know when they are making profits or taking losses. The unit of account allows all the disparate elements of a business to be combined into one number of great significance. If double entry bookkeeping stopped working, society would crumble. Fortunately, most of society can ignore this, since it is not going to stop working.) And in practically every case, that means an item's sticker price will be denominated in the same unit. This allows us to take "money" out of our pockets and pay for something in a store. So most businesses in the U.S. use dollars, companies in Europe tend to use Euros, etc. This, currently, is the primary difference between the money in your bank account and the shares in your mutual fund - one has a fixed price in terms of the unit of account, the other has a market price that changes from moment to moment.
We can imagine a world where dollars are used as the unit of account but dollars are not used as the exchange medium/store of value by thinking about a world identical to ours except that all payments were made by check or debit card, and that all checks and cards were associated with MMMFs or stock mutual funds, etc., where value is stored as stocks or bonds or whatever. These concepts came bundled together in traditional money, but they could conceptually be separated, and as payment systems have advanced, the connection has become looser.
From this standpoint, bitcoin doesn't look like money, but nothing looks like money. From here, bitcoin looks like a digital commodity. It's big advantage is that it can be transported by wire, radio, or any other medium of communication.
What would need to happen for bitcoin to become the unit of account for some business? It would have to be true that this business did enough of their transactions in bitcoin that this approach would be easier. For a retail business, that would mean most of their customers would walk in ready to spend bitcoin, and most of their wholesale suppliers would be willing to accept bitcoin. Also, the unit of account becomes less useful as its value (in terms of commodities) becomes less predictable. Double entry bookkeeping doesn't work well if the value of a business's inventory varies wildly in terms of the unit of account. Hyperinflation requires store owners to frequently update their books and alter their sticker prices (or stop putting prices on goods, which also reduces efficiency). And that is simpler than the case where the value is varying wildly in both directions. So, for bitcoin to become popular as a unit of account, FRNs would need to experience strong inflation or outright collapse, and the average value of commodities in terms of bitcoin would need to experience a period of stability. This will be difficult, if not quite impossible. First steps would include a) bitcoin becomes widely acceptable and widely used, and b) bitcoin's value stabilizes in terms of conventional currency and other commodities c) conventional currency collapses, while bitcoin stays stable with respect to commodities generally. Note that if the collapse of the conventional currency boosted the commodity value of bitcoin, this might actually delay or even prevent businesses from flipping over to using bitcoin as their unit of account.
Can bitcoin become widely acceptable without displacing traditional currencies as the unit of account? Transfers of bitcoin are potentially very convenient. I think what is needed is an application that allows the parties to a transaction to easily determine an agreeable exchange rate between bitcoin and conventional currency. This seems doable, though it is not clear that either conventional businesses or their customers will see much advantage to using it.
In this post I've laid some groundwork but not yet found the answers I am looking for. Rather than delay posting, I want to post this now and I hope that I can finish the job in a future post. Meanwhile, please comment if you have hints, questions, or suggestions. To reiterate, the question I want to answer soon is: If somehow bitcoin became a widely used medium of exchange in the US, but the dollar remained the unit of account, would that limit the central bank's powers in any way?