Possible but unlikely. Part of the personality disorder is that they believe themselves to be different from other people, often superior to other people. The narcissist is in denial about so many of their problems. They are not likely to believe that they are addicts, or that their choice of substance was having any negative effects on their lives. They may go through the motions of rehab, counseling and therapy, but only because they got caught and they see these options as better than jail time or some other consequence of their addiction.
They may learn some new words, phrases, or behaviors from their time in rehab, using the language of addiction and recovery as new terms to toss into their word salad and manipulate people with. Just because they are using new words to manipulate, exploit, and abuse you with, please don’t assume they have changed for the better, or stopped being exploitative and abusive. Usually they’ve just learned how to be more effective predators.
The narcissist may actually give up the substance, if she or he finds a better ‘high’ to be gained by exploiting people in recovery, by elevating themselves to some sort of leader, healer, or guru status within the recovery community (narcissistic ‘sponsors’ may enjoy manipulating their sponsees. Narcissists will enjoy the attention and praise they get at meetings for sharing their crazy ‘recovered addict’ or ‘stuff I did while using’ stories, etc.)
I have heard and read of narcissists going cold turkey on their substance of choice, be that drugs or food or alcohol, and many of them do have the strength and will power to give up something completely. BUT only if they have a new ‘high’ to jump to. Drugs to cigarettes. Alcohol to sex. Food to high-status and praise. From drugs or booze, porn or food, to power, attention, energy, excitement…..basically, they’ll just trade one addiction or obsessive behavior for another one that is possibly less self-destructive or, more likely, less socially-unacceptable. Their defective brains will always be seeking some kind of ‘high’ whether that’s drugs or drama.
Use the time and peace you have while the narc is away in rehab to get your own help and counseling and seek a calmer, happier life for yourself. They may change ‘habits’ or change tactics, but they aren’t likely to stop being narcissists as a result.
=======================
They were monetized but I am giving them away for free here.
If you feel inclined to support my writing, here's my paypal
And if you prefer to pay it forward, I recommend Safe Place as an excellent place to support.