Is it possible to play the G6 on an alto saxophone?
Yes, it is most definitely possible. These are called altissimo notes. A very thorough resource for woodwind fingerings is here.
However, to play these pitches, you need to do a lot more than just put down the fingers and blow (which you can get away with for all of the "normal" notes). You need to voice the notes correctly, which means using the shape of your mouth, throat, and the position of your tongue to support the correct overtone. Otherwise you'll get some kind of out-of-tune honk in the lower register, or some uncontrolled squeak. Practicing playing overtones of your lowest notes is a good preparatory exercise for playing altissimo.
I found a fingering chart that does include the G6 fingering. It can be found here.