On the bus we fly all our ILS's with both auto pilots in so Cat 3 Dual is always annunciated irrespective of whether it is a Cat 1 or Cat 2/3 auto land (Cat 2 is always auto land for us). Clearly on a Cat 1 approach we would disconnect and land manually.
If you have planned a Cat 1 approach then that is what you fly. If you achieve the required references by DA then you can continue to land. If you do not achieve those references, or lose them below DA then you go around. It is that simple.
To do otherwise would be fool hardy in the extreme as the airfield will not be safeguarded, you will be busting your briefed minima and will not have pre briefed what you are up to.
Now if you are in some kind of dire emergency then that would be different but it would need to be dire.