With some crafty driver writing and small mods, it "Possibly" could be made to work,
Power would be the biggest concern, not sure if you could get enough to power out of the parallel port to drive even the smallest of USB flash drives.
You could re route power from the inside of the computer if you never intended to use that port it anything else.
Second would be transfer rate, not sure you could even talk to the USB device at a speed it could utilize.

I have seen some hardcore EE types do some insane (In both practice and concept) things.

USB only needs 2 pins for data, 2 for power, the data paths could be made, the last hop to the USB device is a PS2 adapter with 6 pins, two for power would be just right)

I have seen two computers share files over barbed wire, the question essentially comes down to spend countless hours proving a concept or just accept because it fits does not mean it works.

So as it stands, NO, if you REALLY wanted to, most likely.