Oh that's a really neat theory! So many regularly declined nouns and related word classes end in the sigma. It certainly makes sense considering the frequency of -s ending words. The rough breathing mark seems like it could have played a similar role.
(At least, you have the singular nominatives of the 1st declension masculines, all the 2nd declension noms and a fraction of the 3rd declension noms. And then the singular genitives and the plural accusatives and datives. And so on. Using a 2nd person singular verb, you could probably make a complete and rather complicated sentence in which every word ended in sigma.)
I think the word-final sigma has been found in manuscripts dating to the 1st century BCE, but I think its use was only in cursive and not universal. So, I think you're basically right; certainly majuscule scripta continua documents like the Codex Sinaiticus or Vaticanus wouldn't have used it.
σ is normal sigma and ς is for the endings of words.