SHORT ANSWER: Not really sure, but it wouldn't be all that surprising if they retained their drug habit.
Long Answer: This is a really awesome question I've never thought about before, so kudos to you for bringing it up. I want to preface that I'm not professionally versed in the field of neurology, so I might be able to shed some light on your question only in the context of dementia. (So anyone who is more familar with memory and amnesia, please correct me or add on as you see fit!) So to my understanding, dementia affects a number of areas in the brain, among them the hippocampus, which is responsible for long-term memory storage. However, there is a patient known as Patient H.M. who has actually had his hippocampus removed and was still able to form new habits even though he had no recollection of having formed those habits or, really, any ability to form new memories at all. They managed to discover this when his wife began to bring him out for a walk each morning. This continued for several months until one day, she forgot to bring him out. He was previously unable to find his way back home alone and she panicked and went out looking for him. She later found him in the house sitting in the living room, having had no recollection of what happened. It turns out he had gone out on his own and returned. Amazingly, he was only able to find his way home if he took the exact route his wife always took him on. If he deviated even slightly, he would be unable to find his way back. Following this, they tried to figure out what area of the brain was involved in this process, and they determined that another portion of his brain, the basal ganglia, may be responsible for this. To my understanding, the basal ganglia remains mostly untouched in dementia. I want to mention at this point that there are different types of memory, among them procedural memory which may play a very close role with habit formation. Procedural memory is stored in the hippocampus, so it's uncertain right now as to what extent the hippocampus versus the basal ganglia play in habit formation. There's also the added uncertainty that comes from the question of whether the basal ganglia always plays such a strong role in habit formation, or whether Patient H.M.'s basal ganglia "grew" into that role to fit his needs that arose from his lack of hippocampus. So to finally try to answer your question: If a person has forgotten that he or she has a drug addiction, would they still retain the habit (assuming their basal ganglia is intact)? I can't say with 100% certainty, but it wouldn't be very surprising to me if they did. I'm wondering if anyone with more experience in memory and drug addiction might be able to elaborate on this, but I hope all of this is a good starting point and that it helps a little.
(Also, I'm at work on mobile right now, so I'll update with links to references when I get home.)