I routinely plug in my external hard drive and back up my computer, backing up Microsoft Word docs. Will my Scrivener documents be backed up at this time (from within the Scrivener program), or do I need to routinely export them as Word docs and use that file as a backup?
That depends on how literally you meant the wording in the question. You state that you use an external hard drive to back up your Microsoft Word documents—and if that is the case, then no, you are not backing up your Scrivener projects, nor anything else on the computer save for files ending in .doc or .docx. I’m not sure if you mean it that literally however. Whatever the case, Scrivener projects are just folders with a bunch of normal files in them, so most backup utilities will have no problem whatsoever in keeping them backed up. Some people do like to do periodic “hard backups” as well, by using the compile feature to create a single document file of some format, as a separate backup. It certainly doesn’t hurt to do that in addition to other things.
I would also strongly recommend that you test your backup method. It is often the case that someone thinks they have been backing things up, but when things go wrong it turns out that they can’t restore after all. Perhaps the backup media can’t be read, or they have misunderstood the procedure or they have been saving the file to the wrong place.
So create a test project - fill it with text so it is similar to a real file. Back it up. Now delete the original and see if you can restore it from the backup successfully.
Also think about what happens if you get a corrupt or damaged file. You might back it up before you notice. Then you are in the situation that both your original and the backup are damaged. You might want to preserve several backups so you can find one that pre-dates the corruption.
This is SO IMPORTANT. I bought a new external hard drive, with an automatic back up facility. When my computer crashed - irrepairable - I thought I had all my work saved. BUT, the back up had stopped working (!) several months previously. That was quite a blow. I now have several back up external hard drives, an automatic back up with my ISP AND drop box. 