You did not not mentioned in your question what are the destinations ( Departure - arrivals ) , what is the airport, and what is the Airline .
Regarding batteries or electrical appliances , you have IATA regulations, Local country regulations ( including customs ) Airline regulations AND Local Airport regulations ( In more or less that order - All Apply and differ . Surprisingly so - also in relation to the AIRCRAFT itself ! ).
IATA-> Airline-> Airport-> Customs - they are all factors .
If you really want to know the exact answer in your case - you should ask the respective authorities regarding your itinerary and bike .
That being said - you have already identified the problem yourself - and it is the Battery. Without the battery, the bike itself should have no problem - I might even venture and say that technically you could even take it into the fuselage ( depending on size ) .
I fly a lot with batteries and electronics ( work related ) and I must say that there is no ONE rule that I could identify to fit all situations, except that the bigger ( physically - not necessary capacity ) the battery is - the more problems you will potentially have .
For example - In Guangzhou Airport in China they do not allow any type of " power bank " on board - and on the contrary they do not allow any kind of battery in cargo if not certified and sent by private ( not company ). My laptop battery and the "power bank" are of same capacity and kind . one was allowed - one was not . When I tired to cargo my spare laptop batteries - It was disqualified sent back to my home . When I cargo a whole laptop ( with battery ) it was OK .Note that in that case I mean CARGO and not HOLD LUGGAGE.
In India they confiscated 9V batteries from my devices . but allowed A much higher capacity Power bank.
Regarding the mentioned capacity.
I have already flew ( on board ~! ) with large batteries - One being 320 W and one 200 W . I was pre-approved and checked with local office before the flight.
When I ship cargo with company and Valid Certifications ( CE, CL, UL etc ) - there is no problem usually.
Go figure ...