The A1200 IDE interface shouldn't have much trouble keeping up with 4 writes at a time at floppy speeds - at 2 minutes/disk that's still only a sustained write speed of around 30kB/second (by my in-head calculations). Since the floppy drives are handled mainly by the custom chips, Amigas have always been very good at using them while doing something else. I've never used more than 2 at a time, but you could certainly copy to/from both without and signs of stressing the machine.
Edit: Of course, it will depend on the ADF-making software supporting such an operation... I've never tried making an ADF from anything other than DF0:
