Yes. I know several familes that have immigrated to the United States, and with sheer will have survived and prospered.
My wife's parents broke out of concentration camps, walked the Killing Fields of Cambodia, and managed to get sponsored to the US by a church. They worked their whole lives at menial jobs just to get their kids through college. Now their oldest is a pharmacist, the second oldist is a Physician Assistant (my wife), their son has just graduated and about to start his own business, and their youngest is almost done with college. They were encouraged greatly by the kindly church members who taught them to read using the Bible and provided them a home environment for several years as they got back on their feet.
Another of my immigrant friends escaped to the US by carrying her two kids across a river and finding a way to the US. She worked as a flight attendant for many years until listening to Anthony Robbins tapes. She gives him full credit for helping her start a real estate business which just allowed her to retire from her flight attendent job. She is also now starting her own financial services business and making pretty good money at it. By the time she retires, she will have great wealth. And that is an entirely true story.
What these people had in common was great tragedy in their lives, but also were given a second chance. And when the chips fell, they decided they wanted to succeed badly and weren't going to give up. I think this is a common trait in many great people's lives, coming from poverty or great disadvantage and working extraordinarily hard to make themselves succeed against all odds.