As others have said, it is possible to remove the HDD without moving the logic board. And the antenna board can also just be rotated out of the way.
However, I found it impossible to reseat the new drive (a Crucial m4 SSD) into the correct location without moving the logic board out a little anyway. I just couldn't get the bumper screws lined up in the top slot. This is on a mini i5 with a single HD (now SSD). In the end I got it done, but this step was much more difficult than I expected. Perhaps it is easier when there are dual drives?
I also initially caused the SSD connector to disconnect from the logic board when tightening the Antenna screws back up (step 8). So take care and do this slowly and check everything is aligned!