The following information is from Stackoverflow (License: CC BY-SA 3.0):
Reading the source code in the LocationProvider class, seems that at boot, time is retrieved from NTP server and "injected" in the calculations. AFAIK each GPS sat has a very accurate atomic clock, and every one in the constellation is synchronized to the so called "GPS time". Once the receiver has got 4 or more satellites, it solves (by some method) an equation where there are four unknowns: x,y,z,b; where (x,y,z) is the receiver location, and b is the time difference between the receiver internal clock and the (correct) GPS time. Once it has a a fix, the receiver clock is synced with the correct time.
NTP signal is not directly used to obtain the GPS fix. But for an accurate fix you need very accurate clocks. We're talking nanoseconds here. GPS satellites do transmit current GPS time, but even as it travels at speed of light, there is some delay. GPS receiver has no way to know what the delay is, so it has to approximate from several received signals. With every transmission received the clock get more precise. So the better time you have at the beginning, the less time signals you have to receive to have an accurate clock.
Please report it in the bug tracker of FasterGPS.