The scanner does have a separate power lead. I'm very familiar with the scanner. I have the similar model Fujitsu Scansnap and the wifi worked from the start. This scanner uses a special Evernote wifi set up utility. I can't find help from Evernote or Fujitsu.
I can get the wifi to work on my Scansnap Evernote edition software and scanner. Followed the instructions, used the wifi set-up tool and everything seemed to work. When I unplugged the USB cord, the wifi stopped.