No reason this couldn't work -- just boot your other PC in the DOS version of your choice, do "format/S" on the 2.5" HD (*don't* accidentally format your regular hard drive... in fact, disconnect it first, just to be sure), and copy over the bios update files. The laptop should boot in DOS off the hard drive... which isn't as weird as it sounds; there were lots of DOS machines with hard drives back in the day.
...Except that, I guess, there's a good chance that you won't find a DOS that will recognize the USB HD adapter. In that case, you'll have to try the same trick using a spare IDE drive, then use ghost or g4u or something to copy *that* image onto the 2.5 HD.
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...Except that, I guess, there's a good chance that you won't find a DOS that will recognize the USB HD adapter. In that case, you'll have to try the same trick using a spare IDE drive, then use ghost or g4u or something to copy *that* image onto the 2.5 HD.