No; counterfeit currency is paper notes printed in excess of specie. You can have that with private currency, but governments do it far better, especially when they have a monopoly on the production of currency. Jefferson’s concerns would have been completely obviated if the government had made fractional reserve banking illegal. Currency was, for a long time, nothing more than warehouse reciepts for a weight of precious metals; as such, the printing of excess notes was known to be fraudulent.
Unfortunately, the state enabled fractional reserve banking for its own ends, then began arbitrarily to set the value of notes, then finally detatched currency from specie altogether. The problem was not private currency. The problem was that the state, as always, failed to protect the property rights of those who held currency; in fact, they themselves became the biggest violators of those rights.
If banks acted solely as holders of specie, issuing notes exclusively as reciepts for physical money; and if the issuance of excess notes were recognized and prosecuted as fraud against prior holders of a bank’s currency; and if, most importantly, there were free entry into the market for money production (and therefore the abilty of the market to choose the best, most reliable issuers of money by enabling the free choice of consumers), there would be no problem with money.
The boom-and-bust cycle would end, and the state would be deprived of its cleverest tool of wealth confiscation. And that is exactly why we have no such system; why the state has arrogated to itself a monopoly on the production of money, and the exclusive power to determine its value. Certainly not because it is in the best interests of regular people like you and me. It is absurd to believe that those in the government, by controlling a monetary monopoly through its exclusive ability to use legalized violence, could possibly benefit anyone but themselves, and those directly connected with the central bank.