Is this possible? I know people have done it but it sounds like lifting it onto the boat and then having to lift it off yourself when you're there... is that correct?

No they will put it on and take it off. A few hundred baht depending on how the boat drive feels

Yes, they put it on and take it off the boat for you. I would strongly suggest you do not take your bike over to that pitiful island. Although I understand they are working on some of the roads, when I went there a few years ago the roads from the National Park entrance on were the worst roads I've seen in Thailand. The roads were so bad they rent bikes there with special mountain tires on them to handle all the potholes and jutting rocks in the roads. I wish I'd left mine back on the mainland and just rented. It would have been cheaper. In April 2009 we had to pay 800 baht round trip for myself, my girl and the bike. At that time the bikes rented for 300 baht per day.

Yes, they put it on and take it off the boat for you. I would strongly suggest you do not take your bike over to that pitiful island. Although I understand they are working on some of the roads, when I went there a few years ago the roads from the National Park entrance on were the worst roads I've seen in Thailand. The roads were so bad they rent bikes there with special mountain tires on them to handle all the potholes and jutting rocks in the roads. I wish I'd left mine back on the mainland and just rented. It would have been cheaper. In April 2009 we had to pay 800 baht round trip for myself, my girl and the bike. At that time the bikes rented for 300 baht per day.

Still the same. Rent the bike on the island is the best option.