Apple - How secure is Activation Lock on iOS 7 (and later)?
Any method to restore a device, bypassing iTunes restrictions either by using DFU/Recovery or by not using iTunes, would still require that the device go through the setup process. It is during this process that the device is connected to Wi-Fi and verified with Apple servers. This checks the database of Find my iPhone devices, making sure that the device is not listed. If the device is linked to an Apple ID, with Find my iPhone enabled, then the device will show the Activation Lock screen, and the Apple ID of the account with Find my iPhone enabled on the device will need to be entered.
Completely draining the battery would not fix this, since the Apple ID and Find my iPhone state is stored on Apple servers and retrieved during setup, not from the device itself.
Theoretically yes, 3rd-party software could gain access to a device and restore it, however as mentioned earlier the Find my iPhone state is stored on Apple's servers, so this would be of no benefit, and would not be different to restoring using iTunes when the device is in Recovery mode.
Even though a jailbreak has now been released for iOS 7, a device with a currently active Activation Lock can't be jailbroken.