No, there's no chance that we'll start colonizing Mars in the next 10 years. We'd still have a hard time sending men back to the Moon. Escaping Earth's gravity well is not an easy thing.
Plus, take into account that we have no idea how to create habitations on foreign bodies (or hell, even here on Earth), there's no way.
Our best bet would be to colonize the Moon first, then use it as a jumping off point for future manned missions to other parts of the solar system. That would teach us how to build proper habitats to protect from dangerous environments and how to do things like... grow their own food, recycle their own oxygen and water...
Colonizing the Moon would also be a better step because it's a lot easier to get things to and from the Moon than the long trip to Mars. But no, we will not start colonizing Mars in the next 10 years. Not even with SpaceX's achievements.