Yes they will - just leave your luggage with bell services and have them deliver it to your new resort, you will just need to tip them.
My sister moved from SSR to AKV on our last trip - the only problem was they 'lost' her laptop for several hours. Turns out bell services at SSR said they sent it over, but they didn't. Took a little bit of time to sort out but in the end worked out fine.
Others have simply taken a cab to the new resort with their luggage.