Can Personal Books be accessed and read on a mobile device? At this point unless I'm totally missing something it seems like they can't and are only available on my desktop application. Is this correct? Will they come to mobile?
Correct. Upload and download is being trialled with 5.3 beta on desktop, so i think you will see them coming to mobiles.
As Dave mentioned, personal book sync is currently in beta. However, personal books on mobile will require an update to the mobile apps themselves. There is no stated time table for that to occur.