Do you need fractional reserve banking with cryptocurrency? The physical object limitation of hard currency simply doesn't exist.
But the real hallmark of FRB is that banks only need hold in reserve a fraction of their depositors' account balances. I don't see how CC would change that requirement. As scary as FRB is, without it lending would be a much, much more limited activity.
Money is funny - it's just an IOU. An IOU blown up to massive scale, obviously, but since a business sets the price of something and the market determines if it fits well in to a tradable value comparison, then I don't see how a digital IOU is any worse than a paper one, considering how little that paper is worth when everyone decides it has no value.
And let's be honest. If the value of paper can crash when people agree it has no value, it's just as easy for everyone to agree gold isn't worth a lick either. So in the end, we're just choosing a representation of an IOU we all agree upon, and if that's paper, rock, or digital (or 4 ton coins [0]) what does it matter, in the end?
(This all presumes some degree of safety in CC - with the recent value of Bitcoin thefts, people would ditch it really quickly on a national scale.)
/rambling
[0] http://en.m.wikipedia.org/wiki/Rai_stones