No, you cannot use the parallel port as a serial port. And if you plug a serial device that is capable of supplying the serial voltages you are at risk of blowing the parallel port parts.
Your choice is to get a parallel to serial converter and use the parallel output of the printer port to drive it and the printer. That will free up your serial port.
This is conditional on the software you are using. It is possible that you are locked into a serial port, in which case you are out of luck.
Ed Fair
Give the wrong symptoms, get the wrong solutions.