By direct analogy physical paper dollars cannot handle the transaction velocity in the NYSE financial markets or even the M1 / M2 accounts like checking and savings accounts, therefore the paper dollar cannot be the currency of the USA. I mean paper money at the small denominations currently issued would literally catch on fire if it moved fast enough to keep up with HFT.
You could get away quite easily with BTC only as a partial M0 currency or more interestingly as a (partial?) M3 reserve.
By partial M0 I mean we can abstract this "physical money currency" thing into paper bills and metal coins. Issue paper money down to thousandths of BTC as BTC certificates where theoretically one BTC worth of paper can be exchanged for one electronic BTC. Much like American Dollars used to be precious metal certificates.
People will have plenty of fun wat the expense of the BTC as M3 idea but fact of the matter is you stick something volatile and non-volatile together tightly enough and it averages out a bit. So the real question isn't what happens to Icelands M3 when it becomes as volatile as BTC, but what happens to BTC when its welded to comparatively non-volatile Icelandic economy. If that kind of welding happened, BTC prices couldn't vary more than a percent per month or whatever. That's likely to drive BTC traders nuts because they make piles of dough off volatility so the people most in tune with BTC will very loudly hate the idea for self interest reasons, even if it would be a good idea for a mere 99.999% of the rest of the population. As for the partial idea, much as large banks keep literal tons of gold tied up in vaults, its quite possible for the Icelandic treasury to keep a pile of BTC tied up as one of numerous forms of reserve and that would certainly kill price volatility of BTC or at least drag it down to precious metals levels of price volatility.
There's also the issue of putting on a show. The US Mint issues plenty of legal tender gold and silver coins, but those coins are not a major part of commerce. It would be trivial for the Icelandic treasury to allow payment of income tax in BTC or something similar that doesn't really change anything but makes some nice BTC related headlines. Frankly this is the most likely outcome. Perhaps you'll be able to buy a ticket for a tour of the Icelandic Dept of the Treasury with BTC, and this will be trumpeted very loudly, not much further real world impact. Yet it is a baby step along a path, and the result of buying tickets today might be in a decade everyone will pay taxes with BTC, who knows.