When the mind is on, there is dreaming. When the body is on as well, it’s called waking (waking-dreaming) and when the body is off, it’s called dreaming (or dreaming-dreaming).
When the body is off and the mind is off, it’s called deep sleep. But what is it called when the mind is off and the body is on? Gaudapada does not address this ecstatic orgasmic state.
It is certainly sexual, and possibly that’s why it’s ignored in his extremely logical presentation. Tantra is not Advaita's thing. Also, it’s not in the territory of dreaming, which is one of the main points of his karika.
If this ecstatic state of the body-mind is to be included, then turiya is not to be called turiya but the sanskrit equivalent of the fifth. Other than that, nothing changes. Brahman is beyond causality, the world is still maya, and all is atman.