Paper notes would definitely be worthless since there would likely be no functioning or legitimate government to give them intrinsic value. Also, I doubt anyone would be willing to exchange vital supplies for some pieces of paper.
But it depends on what you have in mind for a new currency. Until the supply situation stabilizes, there would be no way to justify symbolic currency. After scarcity is less of a problem, I think people would shift towards something analogous to gold (cigars or sea shells are historical examples) that is difficult to obtain and therefore usable as proof-of-work. Once a government is established again, and they have decent regulation, control, and activity within the economy, they can start dictating currencies.
You could also have a ledger system where no actual currency is used, but a central record maintains how much everyone produces and how much everyone takes. This would work well on a small scale, but would be infeasible on a larger trade scale.
When a new de-facto currency does eventually exist, it would probably be something hard to obtain like a rare metal or an expensive manufactured good. Or maybe everyone would just barter until the government introduces a currency like gold coins.