Will Removing the back box and replace it with another loud exhaust affect fuel consumption?

No, it will just sound loud. If you remove the cat pipe then it will affect fuel consuption.

If it's just the back box, it will just sound boy racerish. Answer- Having done this myself I think there was an effect on fuel consumption. By replacing the back box and replacing it with a sports exhaust you are increasing the air pass through in the engine and if you get more air in then your ECU should put more petrol in to keep the mixture the same.