No. AO doesn't pay attention to lighting at all. It calculates occlusion by sampling a bounded hemisphere, looking for stuff nearby. When nothing is nearby, it generates a 1. When stuff is nearby, it generates numbers closer to 0.

Why should AO be ignored if a particular light is shining on it?

Of course if a light is shining on an area producing an AO shadow, that light will make it less dark. But it will not make the AO shadow go away completely, because it shouldn't.

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Renderosity forum reply notifications are wonky. If I read a follow-up in a thread, but I don't myself reply, then notifications no longer happen AT ALL on that thread. So if I seem to be ignoring a question, that's why. (Updated September 23, 2019)