Even if the Fire does not show up in ADE, you should be able to transfer files by 'sideloading'; that is copying the files from PC to Fire using a separate file manager such as Windows Explorer.
You may still need ADE to do the DRM bit of accessing the .acsm file and downloading the DRM .epub file. Then copy the .epub file. You should then be able to read it on Akdiko or Bluefire apps (both free) as long as they are properly registered with the same AdobeID. I never had any luck with using the Overdrive app to read bought books transferred this way.