Do cells phones put out a signal when charged through data out?
Typically, no. The USB charging standard has the Data Pins tied to ground or each other through resistors to indicate what type/capacity charger the phone is plugged into, to let the phone know how much current it can pull. While connecting the phone to a regular USB Host also does not have that information by default (phones using non-standard drivers other than USB Storage might have it, varies by manufacturer).

While phones have charging circuits that are already built for efficiency by switching into trickle charge mode once done charging, you can either passively or actively sense this. One way would be to have your charger measure the current draw, to figure out when the phone went from high speed charging to trickle charge mode. Another is to use bluetooth (preferably Bluetooth 4.0 Low Energy) with a custom app/service that signals the charger when the phone is fully charged.

Both options would, IMHO, require that the phone be unplugged and replugged in (or a button pressed on the charger, or on the app for bluetooth) to start charging again, so that means it would discharge as if it were unplugged. Hope that helps.