They can of course do whatever they like once they default and are forced to go off on their own to protect the rest of the Eurozone. I'm sure having a currency of their own again may sound tempting considering their current predicament.
But current cryptocurrencies are popular only because of the promise of easy wealth to early adopters. The concept of taking control away from established capital and the concept of states is only interesting as long as such adopters have not yet become established themselves. A state backed cryptocurrency will not have that dodgy get rick quick appeal so it's hard to see who will benefit from this.