Yes, you need to check out of ASM when you are ready to leave in the morning. You can give your luggage to Bell Services at ASM and ask them to deliver it to the Poly. Then just go to the theme parks until you are ready to return to your resort, then head over to the Poly. You check in there and check with bell Services about your luggage. If your room is ready and your luggage has arrived, then you can go to your room and call Bell Services to bring up your luggage. Be aware that Bell Services can take a while to get the luggage moved, so you need too carry anything that you might need during the day.
Another way to do this is to get a cab from ASM to the Poly after checking out of ASM. Then you check in to the Poly first. If your room is ready you can go straight there and then go about your day. If not, store your luggage with Bell Services and go about your day. The Poly CM's will text you when your room is ready. You can then return whenever you want to settle in.
That said, if the Poly were available for the first night, I would stay there and not move for the sake of one night. It is really nice to get up in the morning and be settled at your resort and ready to enjoy your vacation.
However,
Either way you decide to go, it is not difficult to move and doesn't need to be time consuming. WE do split stays all the time. It is really easy.
Enjoy!