No. It will only sync with the phone that has the same Apple ID. You can set up a shared Photo Stream album that she can access on her phone.
Creating a shared photo stream is as easy as selecting the photos you'd like to share and providing email addresses of the people with whom you'd like to share. You can share from any device using iOS 6 or later; from a Mac in iPhoto 9.4 or Aperture 3.4 or later; from a Windows PC with Windows Vista or later and iCloud Control Panel 2.0 or later installed. Learn more about creating shared photo streams.