They have already done so. They even went so far as to sponsor so-called freedom fighters all over the globe with the newly printed "authentic" US dollars (starting from the Soviet-Afghan war in the 1980s). Needless to say, that these dollars are forbidden to enter the territory of the US...
I have never heard of these type of US dollars, can you provide a link or citation?
These are essentially the same dollars, but their serial number ranges are being tracked (on the pretext of them getting into the wrong hands). Actually, this is no longer a secret...
That link is about bank wires only correct?
That should be about Terrorist Finance Tracking Program. An interesting quote from there:
As you can see, they don't even care about the money entering the jurisdiction of the US. If you asked about cash flow, you can rest assured cash is being tracked too...