My boyfriend has problems with impulses (sex/drugs/alcohol)

He is such a great person and has a lovely heart- Extremely helpful to people and very outgoing and social. We dated for a few months before he broke it off to return to his girlfriend. I also started seeing other people until we found each other a few months ago (we had always been in touch as friends) and realized that we've always been in love with one another.

Just recently, I logged on to facebook on his computer and came across some of his texts and messages to other women. Basically, he was having strongly sexual banter with a few of them. It wasn't anything but sexual, and these women do not even live close to here, so nothing else happened. No video chatting happened. No photographs were exchanged. However, it was enough to cause me some deep pain and confusion. I confronted him about it and he confessed that he always has these strong impulses for engaging in reckless sexual behavior and drug use, but that over his years, he has learned to "dampen" them- he never acts upon them, but the impulses don't ever completely stop. He has used drugs (cocaine and marijuana) in the past. His drinking is not bothersome because it is rather infrequent (two-three times a week) and he is always in control of his mind.

He has had fulfilling relationships before- in fact, his ex and him were planning to have a family a couple of years ago. He is close to his family and is an ideal grandson to his grandmother. However, his behavior caused me a lot of concern. When I talked to him about it, he admitted that he is "turned on" by the thought of having sex with different people but that he loves me and this relationship much more than the high that he'd get from engaging in such behavior. I set my boundaries and requested him to go to therapy to deal with his issues with him impulses. My question is, do the impulses themselves stop occurring at some point with therapy? Can such people have healthy, happy romantic relationships?