No, because the bank can borrow the reserve from another bank. That's the whole point of the overnight market.
But what if no other bank has any reserve to lend? Why then you have a banking crisis as collectively the banking system is short of reserves, at which point the Fed steps in and injects whatever quantity of reserves are necessary to make up the shortfall. So the idea that the Fed would allow a banking crisis in order to limit reserves to some arbitrary quantity is ludicrous. The Fed was created to make sure banks always had enough reserves. That's why we have a Federal Reserve system in the first place.
And in fact there are guarantees -- the bank can take a government bond and automatically borrow reserves with the bond as collateral, directly from the Fed, so the Fed stands ready to convert any bond given by the banks into reserves whenever the banks want. This is the repo market, so you don't need to borrow overnight from another bank if you have a treasury bill or bond, you can borrow your reserve directly from the Fed itself.
https://www.newyorkfed.org/markets/domestic-market-operation...
In short, the Fed controls the price of reserves -- the interest rate paid when borrowing reserves -- and it stands ready to provide banks with whatever reserves they need at the policy rate. Thus the Fed sets the price, and lets the quantity float.
You may also be interested in other nations such as Canada that have eliminated reserves and switched to a corridor system.
That the Fed doesn't care about monetary aggregates is aptly described in this FRBNY note:
https://www.newyorkfed.org/aboutthefed/fedpoint/fed49.html