The IIgs' smartport allows you to have 2 800K drives (mapped to slot 5) and 2 140K (slot 6)... if you really want another 5.25" drive, you'll need to install a controller card and set the control panel accordingly.

As far as the HD20 is concerned, it definitely won't work with the IIgs' floppy port. I don't know if you'd actually wreck anything by trying it, but I wouldn't take the chance.