Yep, used to use parnet myself back in the day, with a home made cable and everything. At one point, my HDless A600 had a custom boot floppy that mounted ParNET and then used the A1200's HD for the rest. It was just as slow as floppy disk but at least swapping them was a thing of the past.
These days, I use a LAN and it's by far the most convenient method of transferring data. However, you need the requisite hardware and software for that to work.