This comment isn't specifically about naltrexone, and might not be relevant here.

This is an example that may provide some vague suggestive evidence that lack of opioids sometimes doesn't help overcome addictions.

I used to really enjoy video games. I used to want to spend almost all my time playing video games. But then (for unrelated reasons?), I developed a bad case of anhedonia. Over a period of several years, I gradually lost the ability to experience pleasure, to the point where I was almost entirely incapable of experiencing any form of pleasure. Video games weren't fun anymore. Playing them usually involved lots of stress, but no fun. But I was still addicted. The addiction got even worse when I started playing the Flash games at Kongregate. That site tracks your achievements across all the games, and often has challenges that are only available for a limited time. Now the previous addiction to positive experiences was replaced with an addiction to avoiding negative experiences. I was now addicted to not failing to earn these achievements, even I knew they really didn't mean anything, and even though the games themselves involved lots of stress, and almost no fun at all. This continued for months, and the addiction didn't end until after my anhedonia finally started to get less bad. Thanks Adelene! Thanks Alicorn!

So, yeah, that's some anecdotal evidence that addictions can continue despite an almost complete absence of opioids.