There's no stupid question and unfortunately I can't give you a 100%
comprehensive answer. But here are parts:

- a locally saved website copy, which is what HTTrack does, will always be
there. No matter if the origin went down or not. That's for sure.

- The tricky thing, and that's the part I hope someone else with more
experience of this tool, is when you regularly update your saved website copy.
In my understanding, changes to the website, also when the website owner for
example deletes parts, will be reflected on an updated HTTrack copy too. So,
if the source has deleted something, your local copy will also delete that. 
If now a whole website goes down, I don't know what would happen if you would
run the update HTTrack job over your pre-existing local copy.

Hence, I recommend you to zip up your local copy every time before you run an
update job. Just to be sure.
If the result of that run is ok for you, you can remove the backuped .zip
version of it again to save space. And repeat the same for the next time.