Short answer, yes.
Long answer? We have so much research to do, so much innovations that will be needed before such a feat becomes even remotely possible. Why? Where to even begin...
First is the most important: radiation. Because Mars has no magnetosphere, its denizens would not be protected from the background radiation of space (cosmic radiation), nor the blasts from the sun (solar winds). These are things that astronauts (and cosmonauts, and essentially any space traveler) can tell you about, and many have. They tell tales of 'flashes of light as they close their eyes', which is in fact the background radiation striking their retina. This radiation can attack DNA directly, increasing the risk of cancer.
Second up is the lower gravity of the red planet. Yes, it is almost like earth, but it has 0.8G, so 20% less gravity than Earth. This would mean that our muscles and bones would be stronger than the gravity needs it to be, meaning we would lose muscle mass and bone density living there. Though the difference isn't excessive, it is important to keep in mind. Especially when people want to go from Mars to Earth -- their bones and muscles would have exactly the opposite problem.
Then comes the biggest issue: housing. Mars would need a stable habitable area. Check out Mars 1 Project, seeing as they have the idea already.
So, yes. This is possible, and though it is within our current technological reach, we have so much more to learn and so much growing to do as a society. Time will tell when (not if) this becomes a reality.