Since there are 7.8 billion $100 bills in circulation, and the lifetime of a $100 bill is about 90 months, that means there are about a billion produced each year. Your extra two million bills a year would barely be enough to notice.
The conclusion is right, but the argument is wrong. Those billion bills are replacing other worn out bills (banks take old bills to the Fed, who shreds them and returns new bills).
They aren't all
used for replacement. All sources are also from FederalReserve.gov in the paymentsystems directory. (Obfuscating to avoid the spam catcher.) coin_currency_orders.htm says:
The estimated number of notes that Reserve Banks will destroy account for nearly 90 percent of the FY 2013 print order (excluding the quantity of new-design $100 notes); the expected growth of Reserve Bank payments to circulation accounts for the remainder of notes in the FY 2013 print order.
Of course, that small excluded portion does account for over half the value.
Stockpiling an entire series may be unusual, but stockpiling most of a low-demand series (like $2 notes) is apparently normal, so as not to print any in the following year.
coin_data.htm#value suggests that the supply of circulating currency typically goes up by about 1/16 per year, so the "approximately 90%" might just be their default assumption.
It looks to me as though the new hundreds would represent about a fifth of a percent of the intended growth in "circulating" currency, or a quarter of a percent of the intended new hundreds. That is (barely) enough to matter.
On the other hand, one reason for the increasing percentage of value in hundreds is that they are used (largely outside the US) as a store of value, and don't really
circulate much. So (assuming the fakes get spent and not detected and not destroyed) they may well represent a far higher proportion of the actively
They would certainly have an effect if they were all released in the same relatively small town.