The thing is you do not need any onboard database for GLS approaches except for a nice picture on the NAV and Vertical Situation display. The approach path is send out by the ground station and compared on board against the actual position, same as for an ILS.
The channel number is dialed into the NAV receiver, same as a frequency, you just have to change the mode to GLS instead of VOR or ILS.
It is all in all similar to a normal ILS, you select the approach in the FMC database, and you select the corresponding channel number (frequency for ILS) on both NAV receivers.
However i do not know where the actual position computing is done and the following position comparison. GLS is tied into the same control panel as GPS and the IRUs on the after overhead panel as far as fault detection and alerting goes, but not much else is covered in our documentation.