Hi Sapling,
For me prayer is absolutely at the centre of my recovery programme. I am following a 32 week prayer 'retreat'. While it is not specifically aimed at alcohol or other addictions a theme that runs through it is understanding the 'attachments' we have and learning to recognise when we have healthy and when we have unhealthy attachments.
I start the day with 30 mins of quiet prayer using the retreat programme and try to fit in other times during the day and especially at the end of the day (though the morning prayer time is one that I never miss). I'll be going on some weekend retreats as well.
So, yes, for me recovery is absolutely centred upon prayer and God. But that doesn't mean I don't think there can't be other good ways as well.