The website says that "Transporting bikes is not included in your baggage allowance"

It seems that they will always charge for it... and that the weight allowed for ANY sporting equipment corresponds to the baggage weight allowed in the cabin you are travelling in...

23kg for Y and 32kg for Business/la Premiere....

I suspect the only way to carry it within your normal baggage allowance is if it would fit within "normal" baggage sizes....and thus can't be identified as a bike...