Is a back-up battery for GPS aps necessary?

This really depends on your application. Using a back-up battery allows the receiver to store data such as time, position and satellite visibility so the receiver can quickly establish a valid fix and so the same output messages will be active once power is restored.

This is an especially important consideration for users operating a receiver in NMEA mode. Receivers that do not have EEPROM, and without battery back-up the receiver will revert to the native Motorola binary mode when main power is removed. Since many NMEA based software applications do not support the binary protocol, the only way to command the receiver to return to NMEA mode is to use another application to establish communications in binary mode, order a switch to NMEA, and then return to the NMEA application. A battery saves a lot of frustration and re-initialization headaches