After repeated tests, I have concluded that invisibility potions are no longer effective. I first noticed this issue some time during one of the 1.7 releases, and a search through forums has revealed it to have been a problem since at least version 1.6.4
Other players report that AI still responded to them as if visible, including a range of all common hostile mobs except spiders, but in my own experience even spiders responded in agro upon coming into usual proximity with me.