Well, no. It's not "This thing signifies one sound and one sound only." It's a "... What? Okay, that's another one for the ' pile," scenario.
What would be the
point of that. It is assumed that the language in question has both pronounceable and unpronounceable sounds, and the former outnumber the latter (else what would be the point in a Latin orthography anyway). If there are several unpronounceable sounds, it makes sense to have several symbols for them, because while the human readers can't pronounce them, they can distinguish between them, and therefore read (which is the point of a Latin orthography for Chtulhuese).
There is literally no scenario in which the "another one for the pile" approach makes sense. None. If you're going that way, there's no point to having an orthography, since Rule Zero for
any orthographic system is "Thy graphemes shall have phonetic meaning that can be derived from their shape or optionally, position, but it shall be a concrete meaning in the end." If an apostrophe in any position could be any of your, say, three unpronounceable sounds, then there's no point to having an apostrophe. Nothing will do just fine, since the apostrophe does nothing for increasing a reader's comprehension anyway if it has no precise meaning.
On the other hand, if we have several different symbols for Cthulhu noises (' for mandible rattle, " for side-spiracle hiss) then a human reader can distinguish between, say "kth"ha'" 'tree', "kth'ha'" 'forest', "kth"ha"" 'water' and "kth"ha"" 'ocean'. With an apostrophe, those would have been indistinguishable, and you'd get meaningless texts. The meaningless texts would be supposedly written by humans (since they're in Latin). Now you must assume your humans are slightly dumb and can't make up a functional transcription system for Cthulhuese.