IOS – If I disable Location Services, will Find My iPhone continue to work

The only thing that matters on iOS 7 is whether you have fine my phone enabled. Also, you can't turn off location services when you have find my phone active.

If so, you can't get iTunes or the device to erase itself unless you enter the password for iCloud account that is enrolled.

If you do factory erase it, it still won't re-activate unless the iCloud password is entered. So, to answer your question - location services is likely not re-enabled since the device lock prevents activation of the OS and opting in to location services before the wipe. It would either require access to the source code or servers from Apple to know if location is tracked in is case, but my intuition is no.

If you enable lost mode, that locks the device, but it still is traceable and can be located. Just as if you didn't enter lost mode.

If you erase the device, that removes the data and tracking ability once it connects to the Internet and receives the self-destruct message. It still displays the lost message, but you can't track it.

FakeLocation

FakeLocation is extremely easy to use. Just open it up, choose the app you want to fake out and then pick your desired fake location, save and you’re done. It’s as simple as that. To end faking your location just un-check the desired app.

LocationHolic

Fake your iPhone's location with LocationHolic. You can set any location as your iPhones location.