If have a mod enabled that adds something completely optional to the game and doesn't affect the % on the file (let's say the Lap 3 mod for example), could you submit a run with it on if you aren't using anything from the mod itself? this might be a weirdly worded question but I think you'll get what I'm trying to say.

Yes it will still invalidate the run. Any mods whatsoever are not allowed for submission, even if they don't affect % and you do not interact with the mod at all.