Well yes and no. The way you establish a currency is as follows, traditionally: you assume political control over some area of land, and all political power is backed ultimately by military power (tho' cushioned by laws, courts, police, etc internally). Then you declare that everyone living on this land must pay taxes, and they must pay these taxes in... Seashells, or gold doubloons, or tons of flax, or whatever. Hey presto, you have a currency! Later on for convenience sake you can keep all your seashells in a vault and use paper tokens instead.

The thing is tho', you want other countries to accept seashells too, places where you have no political or military control. The way this happens is that those seashells can be exchanged for goods and services provided by your citizens, who need seashells anyway to pay their taxes, so might as well use them for everything else too. Therefore the value of a seashell on the currency market (i.e. outside your borders) is backed by the industrial power of your country.

So to sum up, a military backs a currency only in the sense that the military holds borders in which industry can operate safely - and not in the sense of military as ultimate debt collectors. At least, the Greeks better hope not.