Yes you can. If your transponder has a cable with both the computer serial output connector (a 9 pin connector called a DB9) then you can plug it directly into a serial port on your computer or use a USB-to-serial adapter. You can then use the NMEA output from the transponder (for most Class B transponders these are the orange and black wires from the 4-wire gray cable - check your transponder manual to be sure). Select which port you want to use on the AISWatchMate and connect the orange to the data input for that port. Connect the black wire from the transponder to the signal ground for the same port.
When you hook it up this way, the data from the transponder is sent in parallel to both your computer and your AISWatchMate 670.