I don´t think you are officially allowed to leave the bike behind in a carnet-country (if and when you´ve used the carnet for temporary import). Another thing is, how strictly this is enforced, and will they have a system to notice, that you have a bike in the country, if you´re flying away, for example. But you could face big problems, when you return, and try to continue with the bike. The customs probably would also have the right to claim the taxes & import fees be payed from your carnet deposit, if the vehicle overstays the time they´ve given your bike to stay there legally.
But this is just speculation. Might be worth asking from the carnet issuing body (the AA in your home country, I believe).