No, because people could still find value in the notes. For example, let's say the nation had the most transparent and hard-lined central bank in existence. Then, people of other countries might find the notes worthy.
Of course, there is some intrinsic value to the paper notes as well. But it would have to be assumed that such value is zero, as producing something would raise the GDP.
In practice, the whole case is absurd, but the answer would almost certainly be no, no one would exchange the notes for anything.
As for the mechanics of the question in the comment section, let's consider the case through the equation:
$Y = C+I+G+NX$
And also the central bank's profit/balance sheet:
$\Delta equity = profit$
If the central bank bought some valuables to back it's money supply (gold for example), the investment would raise and NX term would decline, cancelling out and also creating a trade deficit. All of the money would flow outside the country, so no citizen could use the currency to buy anything.
If the central bank itself tried to fund the increase in consumption (or give the money to it's citizens to do so), the trade deficit and consumption would increase. However, the assets of the central bank would not increase (since consumption items depreciate). In the process the central bank would become insolvent as it would suffer a loss. Then, people would not be expected to use the service to an even higher degree. Although, the central bank could try to leverage it's balance sheet, buying investment products from foreign nations to cover for this.
In the case that there was an income stream, such as donations or foreign investments, the government could easily have a solvent central bank and thus I don't see why the money would not have value. (of course, 0 GDP would require that the central bank is operated for free). The question becomes a lot different if we assume fiat currency, but I won't go into that.
In any case, this is a major hypothetical with unrealistic assumptions.