If I disable Location Services, will Find My iPhone continue to work?
No, Find My iPhone will not continue to work if Location Services is disabled. However, if you enable lost mode, it will automatically enable Location Services.  

https://support.apple.com/en-us/HT201357


  In iOS 7, if you turn off Location Services and use Find My iPhone
  Lost Mode, Location Services will be re-enabled on the device as long
  as the device is in Lost Mode. Once Lost Mode is disabled, Location
  Services will return to its previous state.