No, I don't think that an English language learner would benefit from reading the KJV version of the Bible any more than he or she would from reading any other 400 year old work.
Without a strong personal reason for reading the book, the combination of antiquated writing, a lack of a coherent story line from book to book, and sections that can be extremely tedious (ex: the begats) could make wanting to read it more difficult. I personally find it boring and disjointed at best. You definitely don't want educational reading to feel like punishment.
If you're interested in reading something in general to improve your English, then I would strongly suggest finding something that fits your interests. If you're interested in world religions or have always wanted to read the book for some reason, then the Bible might be a reasonable choice, and there are numerous freely available modern translations that would be more appropriate for learning English. If you're not determined to read the Bible specifically though, there are any number of other books that are written in modern English and that are much more enjoyable to read.
If cost is an issue, you might try visiting Project Gutenberg, which offers a huge range of public domain books as free downloads. Most are roughly 100 years old, but the language of 100 years ago is far closer to today's language than the KJV, and people had figured out how to write quality novels by that point as well, so the reading is very enjoyable. Have a look at their most common downloads for suggestions.