And what do you think, does refusal to play (deprivation) contribute to recovery from addiction or is it useless?
Kind of. If you are able to stay away from gambling for some time, it is possible to find a solution to addiction because one may not find gambling that interesting. That is why when you go for counseling to fight addiction, you will be wise not to gamble, because staying away from gambling plays a very important role when it comes to gambling addiction.
Apart from gambling, even when you are addicted to substances, you will be advised to stay away from them. So the same principle applies to gambling addiction: staying away from gambling can be a cure for gambling addiction.