Hitting bottom is the main impetus for getting clean and sober. Hitting bottom is proof that you can't manage your own life. Hitting bottom is Hell. Addicts who want to stay sober have been in Hell (or have suffered enough to see that their addiction is leading to Hell).
We addicts need a strong spirit to get out of that Hell. Following (without truly believing) someone else's religion is not going to get us out of that Hell. We addicts need a personal relationship with a Higher Power. Although one's Higher Power may be a part of an organized religion, the personal relationship is the key to recovery from addiction. The personal relationship is the difference between religion and spirituality.
So, one could argue that the God as you understand him does not even have to be a traditional God of religions. It can be anything that you believe is a power greater than yourself that keeps you clean and sober. It should be relatively easy to conclude that there are powers greater than ourselves. Alcohol is one of mine. The 12 steps are also a power greater than myself and they have kept me sober for 26 years. Isn't your drug or behavior of choice getting the better of you? Isn't it time to call upon a higher Power that can defeat your drug or other addictive behavior that is killing you?
So please, don't walk out of an AA meeting if you hear the word God. No one can foist his or her religion upon you in a 12 step meeting. But do try and follow the spiritual principles of the 12 steps.
Try closing your eyes and asking your Higher Power to come into your life. Ask him, it or her to come into your life to keep you sober. As you go through your day, keep your spirituality strong on a moment to moment basis or else you will head back towards relapsing. In other words, do spiritually strengthening acts like helpful acts, prayerful acts, forgiving acts, loving acts, unselfish acts, pure acts, and honest acts. These actions will keep you connected to your Higher Power which will keep you sober.