Bicycles are included in the baggage allowance, so yes...it may be checked as one of your two pieces (not exceeding 32kg, of course).

Regarding the waiver for excess luggage, I agree it would be a nice perk to give some sort of "credit voucher" when passengers check no luggage that could be saved for future use (e.g., 1 or 2 kg future credit for each flight without bags). However, the accountability of such a system would be hard to manage.