Here's the deal with the external 800k drives and the original ROM. If your drive looks like this:
IE, it's styled like an Apple IIgs or SE and has an eject button, then it will work without a driver, including being bootable. But if it looks like this:
Then it *probably* won't work, and may in fact give you a Sad Mac if you try to boot from it. I say "probably" though because some late runs of this drive (or ones that were at some point repaired) might have the same mechanism as the other drive, which is "fixed" so it works around a bug in the floppy driver in the 64K ROMs that was fixed in the 512ke/Plus ROMs.
If the picture embeds above don't work see this page; the "Apple 3.5" External (A9M0106)" is the "universal" drive that works with everything while the "Macintosh 800k" (M0131)" is the one that needs the HD-20 driver to work on a 64K ROM machine. I know it says the A9M0106 "needs" it too, but it's only needed to be used to its full capacity; it acts like a 400k drive without it.
The 128k doesn't have enough RAM to load the HD-20 init (I *believe* it will in fact refuse to load on a 128k if you try it) so, yeah, if you have an M0130 it's basically useless unless it has the later mechanism installed.