While it's true that the data transmission from all satellites carries the time information (to be exact, the time at THAT satellite), most consumer GPS units won't decode and display that information. Until there are enought SV (satellites) received and decorrelated, the unit will most likely display the time that it's calculated based on time passed from the last fix. Now, when the unit has calculated it's position (minimum of 3 satellites for a 2-d fix, 4 for a 3-d fix), it will also have calculated the Zulu-time for the unit's location (all GPS time is in Zulu/GMT) and will display 'local' based on the device settings.

RFTraveler