If you are claiming a discount for being a sole occupier, then you lose that discount. Probably not automatically - it require some joined-up thinking which not all councils are capable of.
But legally you lose it anyway - whether you add that person to the roll or not. The two are not directly connected.
In theory no. Joined up thinking councils may not have but the right to x-match information they have although I am not sure if the electoral roll is necessarily allowed to be.