I had the network package for the CD32 to my A1200, which used the serial port (via the CD32 keyboard socket!), and it was slow - the software gave the option of different speeds, but the higher the speed, the more likely the link was to drop which meant a reboot of both machines to re-establish.
Parnet will work, so it is feasible, and it will be faster as the Parallel port is faster than the serial but speeds will still be MUCH slower than using a CD rom drive and an IDE interface directly on the A1200.
