My first reaction to this question would be yes, but then I reflected on it for a moment and I have to say the answer becomes no.
Peace certainly can bring happiness with it. There is no argument there, but peace can also bring the turbulence of growth.
Here is what I mean…
If I am hurting and frustrated with something in my life that usually means that I am in a state of emotional arousal. I can feel sometimes in these conditions, that nothing I chose works, that I am beating my head against a wall, or that in extreme instances there is no way out.
In these cases peace provides me with the ability to calm down, think it through, and start taking positive action. These things do not necessarily bring happiness. They always bring growth, but growth, peace, and happiness are not mutually exclusive.
Peace can very much be a tool that helps a person clear their head and take positive action towards a decision. Then the hard part of committing to that change comes in and this is not always a happy thing.
Happiness comes later after the storm has past, after the steps have been taken, and after the growth is adjusted too. Peace is again an agent at work in this case too.
They key in all this is the ability to find happiness again, especially when the change is not something you wanted in the first place; peace is the mentor of this end and when you find you are able to be happy in this circumstance you can find your peace and happiness walk hand in hand.