It's not really possible with USB.
You can do this with hacks on Wifi readers. As long as you have a Linux shell or a custom network aware app running in the background, you can use that to sync files through Wifi, while you read. I could do it with my Story HD, if it was worth my time.
With USB it's a bit different. USB exposes disks with filesystems on them. In order for that to work, the reader itself has to stop using those filesystems itself. Because filesystems are not designed to be in use (mounted) by multiple machines at the same time. There are exceptions (cluster filesystems) but nothing you'd find on a reader.
So all readers have to stop using files while offering storage via USB. And remount their filesystems after USB is ejected/disconnected. Reading during this time would only be possible if the book and everything pertaining to reading was loaded entirely into memory beforehand.