I'm afraid you won't be able to activate Adobe DRM with Wine. The Reader software appears to do something low level with the USB device that needs more driver support than just for USB mass storage. If you manage to do it anyway, please be sure to report back how you did it!
A possible alternative can be to have the U.S. Sony Reader Store create an Adobe ID for you. This works without a Windows host, directly from the Reader:
In the settings menu, switch the Reader's country to U.S. Then connect to the U.S. Reader Store using the button on the home screen. The first time you do this, the store will guide you through the creation of an Adobe ID and activates the Reader.
You'll end up with a new Adobe ID locked to your device that has no password set. To use this ID with other Readers or Adobe Digital Editions (ADE), go to
Adobe's website and reset the ID's password. Then use the ID and the password they email you to activate ADE as well before you use it to download new content.
Warning: This method will render all DRM'd content purchased with other (previously generated) Adobe IDs inaccessible (until you relogin with your old ID). Apprentice Alf may be able to help.
Let us know how it went! Good luck.