Hello, Yes once you register the new Kindle you can then transfer all of your downloaded content onto the new device. This isn't automatic unless you "sync" the Kindle.
More details on how to do this are at the link below:
If you need further assistance let me know. Please do not forget to click the 5 STAR RATING, at the top of the page for my efforts. It is my livelihood and you can follow up at any time if needed.