I have a Macintosh Plus with a broken internal floppy disk drive. Would it be possible for me to take an 800k Macintosh Plus-Compatible external disk drive, and open it up to take the drive out of the casing, and use it to replace the internal drive?
Yes, the mechanics are the same; but there are a lot of models out there that are similar:
http://www.vintagemacworld.com/drives.html
In the mean time, you can just plug that drive into the floppy port on the back and use it as-is; the computer will be able to boot from it and use it as if it were the internal disk
Yep, that's the sort of drive you're after.
Would this drive also work?
http://www.ebay.com/itm/Apple-3-5-800k-Drive-A9M0106-Tested-Working-/27180865117 1
Yep, the A9M0106 will work fine on your Plus.
Macintosh Plus External Floppy Disk Drive Question
