Yes, it can become an addiction. Whether or not it's as bad as some other addictions is debatable though, and also off-topic. To use a (presumably) fictional example, we could look at Don Quixote. For readers unaware, the story of Don Quixote begins with an old Spaniard who spent years and years and so much money on chivalric novels. After a while, he started to believe that the books were historical accounts, and that his life was just like one of the books. Considering how Miguel de Cervantes wrote it, he made it sound like the events had at least some basis in reality. Whether or not this is true, there are accounts of real people showing similar habits, except that they often just buy a large personal library for the sake of having one, more so than to actually read what they own.
Reading can become an addiction similar to alcohol and drugs. It is a gateway out of reality. When you are young and have no access to any illegal items, reading is the next option. I would know, I used to do the same thing. It may seem silly, but I would place myself into the stories wanting to escape reality. I hated my life. I have read over 100 books in middle school just to escape the bullies and difficult life. I know better now, but there are still people out there who depend on reading like a child with a safety blanket. Reading is as addictive as drugs, alcohol and the internet. Be careful and read in moderation.