You do not need to be online to schedule a sync, but the Kindle Fire will not download any information while it is offline. A sync made offline will automatically be performed once the device connects to the internet.

You can remove, loan, clear the page-read data, or manually download a title by pressing the “. . . ” button next to a purchase. Manually transfer your purchases by connecting your Kindle to your computer via USB. Press “. . . " and select “Download and Transfer via USB”. Select your device from the dropdown list and press “Download”. You can use this to get your purchases if you do not have WiFi (but you do still need a working internet connection on your computer to access the site). [3] X Research source

Annotations, bookmarks, and highlights will also be synced across devices. You can also turn on “Automatic Book Update” from the menu below to get the latest changes to the digital edition of your books. Make sure Whispersync is enabled first to ensure your annotations are not lost with the update.