Electrically yes, it is possible. The PC parallel port is a combination of TTL (5 volt) voltage level signals, both data and control bits, some inputs and some outputs and some can possibly be input and output. Complete parallel port emulation takes 17 digital pins, so the Arduino can in theory handle complete emulation, however many devices don't use all the signals so one might be able to get by with fewer pins.
There are lots of references on the web for how this port works. Here is one:
http://electrosofts.com/parallel/index.html
Lefty