I believe that getting sober can be a step toward inner peace. But it also needs to be worked on in all other areas of life. I don't believe that all the people I see walking around every day who have never had a drinking or drugging problem are perfectly at peace with themselves. Maybe some are, others not so much. Sobriety can be just one of many stepping stones. I don't expect that just being sober will transform me into a self-actualized peace machine. I just know that as long as we continue to turn to the drink for answers our journey toward peace will be slowed, stopped, or even back-tracked.
When we give up our substance addictions we free ourselves up to look for other more positive ways to bring peace into our lives. Or something like that.