If the AP OFF warning failure occurs on the subject flight how will you know? You are not required to test it before a LVP approach.
The clue is in italics on that QRH page..
"On ground, the equipment list determines which approach category the aircraft will be able to perform at the next landing." (My bolding).
i.e. On a previous flight the AP OFF warning was inop, entered in Maintenance Log, and is now a MEL item.
Whether the FMA will say CAT3 DUAL.... well I haven't a clue! Can the engineers change a setting?