That depends on a hell of a lot of things, but I think so. The reason I would consider it a possibility is that a bunch of technologies are developing faster than ever before. In particular, reading and writing DNA is now about a million times faster than seven or eight years ago. Another technology that the de-extinction of a Neanderthal would require is human cloning. We can clone all kinds of mammals, so it's very likely that we could clone a human. Why shouldn't we be able to do so?