Tl;dr: There is some effect, but it doesn't really matter.
When people take currency out of circulation, whether it be by saving it or for numismatic reasons, the effect is the same. The overall levels of currency circulation decreases, and that has an effect on the fiscal situation within a currency area. It is for this reason that one of the tools that central banks to stimulate growth is to disincentivize saving (correspondingly incentivizing borrowing) by lowering interest rates. People then move money out of banks to increase the amount of currency, creating inflation and hopefully economic growth.
The question, however, is about whether that has fiscal impact through numismatism involving current currency. Older currency is de facto if not de jure demonetized, and consequently not a factor in fiscal calculations. It is only held and traded amongst collectors as it is.
To stick with the United States as the example, if in a single year the country were struck by a singular fever for numismatism, and every man, woman and child acquired ten copies of every coin and bill then each person would be taking slightly less than $200 out of the economy. In the U.S. that would total nearly $600 billion, allowing for rounding. That would be the equivalent of about 5% of the U.S. economy, which is a lot! The central bank would surely have to take account of such a change in the currency market.
That said, there are many reasons to doubt this would ever really matter. First, this could only happen once, since everyone would already have the collection they wanted, they would have no reason to do the same thing the next year. Second, numismatism is not that popular, and probably isn't even close, and therefore the scale of the effect is much lower, and the more people who collect current coins the less those coins will be worth in the future. If everyone still participated but only got 1 copy, then you are looking at 0.5% which is much less important. Finally, while savings rates vary globally, expecting everyone to suddenly save $200 more than they are now is highly improbable, and in the U.S. It would effectively double more than half of the populations savings rate.
In the end international currency transactions would swamp any changes that numismatism make to currency supply, billions of dollars enter and leave U.S. Economy every day, in oil transactions alone, let alone other banking transactions. Compared to that, even the most enthusiastic numismatism is a mosquito splash on a tsunami.