Only autosaves and quicksaves would get overwritten. Manual saves (You went into the save menu and saved there) will be fine as long as you don't save over them yourself.
Though, if you did find the right save and fixed the issue, then what? You'd still have to redo everything anyway as the fix won't carry into the already existing saves.
Think of it as Back to the Future 2. You have a '1985' that you have this issue in, you go back to the earlier save and solve the issue, but everything you do after that will be a new timeline as it were.
If you found the right save and corrected it, it would be fixed...but only for the save. It's not going to transfer through to all of your other saves. You'd just have to start over from that point again.
happened to me once with Strong while a Mirelurk Queen sneaked up on us. I had to re-load an old save, although the dialog did no immediately appear, i had to wait until Strong opened up again.