Actually no. Apple intended the external Apple 3.5" Drive (A9M0106 – originally introduced with the Apple IIgs) as a universal replacement for all computers, including the 512K (and unofficially the 128K). The Apple 3.5" Drive is 100% compatible with 512K without special software or the 128K ROM. You can boot from it with 400K MFS formatted disks, format, erase and use any 400K MFS formatted disks and even format a double sided disk as 800K MFS. What you cannot do is use it as an 800K HFS drive without the HD20 INIT startup disk, but it will boot from the HD20 INIT disk allowing it to be used as the primary drive with HFS. The internal 800K drive mechanism used in it is also fully compatible as an internal 512K drive. NOT all 800K drive mechanisms are. You can read more about it here.
However, I recommend you both learn to fix your 400K drives and use them when working with 400K files and disk images (I don't fully trust an 800K or Superdrive to properly format the drives) :beige:
You have your choice of a functioning drive, with no special warranties, for a starting bid of $.99 from mercasaurus, or a "serviced" drive, for a buy it now price of $149.84 from from danapplemacman. Obviously the more you know about maintaining your own equipment, the less you have to pay for it!
Presumably you have visited this excellent site already.