The answer to this question is somehow relative. A problem drinker doesn't necessarily mean an alcoholic. So if someone is drinking a bit too much or too often, and can be considered somehow a problem drinker, the answer is yes. Not being addicted means that he can say stop someday without having to go through the withdrawal symptoms and so on. Of course, it will be a bit difficult, like any habit or addiction a person can have, but it is not impossible. With a little help and support from family and friends, and of course, if the person in question is really decided to stop drinking, he can cut down the alcohol for good, or at least reduce it to an occasional drink. Surely, if that person limits the amount of alcohol he drinks but sometimes he can't stop within limits, the best choice would be to stop drinking altogether, because from a little too much now and then he can become an alcoholic.
However, if the problem drinker in question is an alcoholic, the answer is generally no. Although someday he may seem decided to cut down the alcohol and maybe manage for a little period of time, sooner or later he will come back from where he left. Of course, that in this case, cutting it down for good is the only solution, but it won't be so easy. An alcoholic rarely manages to stop drinking on his own. He usually needs some professional help, a lot of support, and sometimes even drugs to help him deal with the symptoms of withdrawal. An alcoholic's addiction is so strong that it can't be defeated very easily. Even more, an alcoholic usually doesn't recognize his problem, and that makes it harder to treat.
If you are not sure if you can just stop drinking. Just consult a professional who would be able to assist you or refer to detox if needed.