Sounds like you won't be renting but if you do, make sure to read the fine print on any rental contracts IF you choose to go past Hana and complete the loop all the way around the south end of the island (same for the north end too). All the rental companies I've ever rented from have stated that your contract will become null and void if you choose to take your vehicle on these roads AND, IF you require assistance while on these roads, they will not be coming to help. However, due to this, the traffic is drastically reduced. I think the paved portion past the Seven Sacred falls, around the southern end would beat you to death on a scooter.
It's not the limits of the bike... it's the limits of the rider on the bike.