Hrm...let me put it this way: yes, it is possible. Almost anything is possible, even within the laws of physics.
Do I believe it is a good route to take to the stars? No. Not at all. Not yet. AFter we have a firm foothold in our solar system and perhaps even Proxima Centauri (if there are habitable planets there).
Based on my knowledge of astro-physics (next to nil, that is) cryostasis and auto-pilot is the direction we need to be funneling our funds to. My idea/plan is as follows:
1) Design a colony ship, one designed to take off once and land once, forming a hub to operate from upon arrival at the destination planet.
--->a) The majority of this colony ship will, in fact, be deep-space survival technology, including cryostasis pods (designed to be reusable: this is expanded on later) and fuel for acceleration/deceleration in the near-frictionless near-vacuum of deep space.
2) Train a crew of five-hundred to crew the ship and take over if the auto-pilot begins to fail. This crew will work in shifts of one-hundred a year. They will be encouraged to have children and train them in the same technology they are, just in case this trip takes upwards of 32,500 (500x60) years.
--->a) Between shifts, the crew will have their own cryostasis pods.
--->b) We'll have to hope the trip takes less than four generations in this style, since inbreeding would be most difficult to avoid after that point, though a generous person might be able to stretch this to ten or even fifteen generations (given that even the products of close incest do not begin to develop birth defects until the second generation).
3) Select colonists based on certain desirable qualities, a mixed bag of leadership, artistic and scientific ability. Ensure a colony of at least one-thousand, possibly more if fuel/weight ratios don't top out.
4) Launch.