The question depends on too many factors. I would say if what is meant by non-believer is an atheist, I would say no to a marriage. The greatest religious impediment to marriage is different and inflexible beliefs and atheism is the most inflexible belief. If by non-believer you mean an agnostic, someone that doesn’t know if there is a God or not, but certainly doesn’t believe in religion, I would say it depended on what good qualities that person had. If by non-believer you mean someone that has no opinion about God or religion but doesn’t practice religion I would say yes if that person had the other qualities that you were looking for in a spouse.
I base my opinion on empirical evidence.
I was a Catholic in name only when I married my wife, a devout, non-judgmental Catholic. Based on my love for her and the sacramental grace inherent of our marriage, I too, have become a devout and non-judgmental Catholic. We raised eight children, educated all in Catholic schools, and provided them with the advantage of being raised in a truly religious home. One became a priest; three married Catholics; three daughters married non-Catholic men none of whom practiced any religion; and my youngest son married a practicing Methodist lady, who converted to Catholicism after a year of marriage. The three non-practicing son-in-laws converted after 12, 15, and 21 years of marriage, the durations of which give testimony of the non-proselytizing, non-judgmental nature of our children. All three of the converted men have told me that the most important factor in their decision to convert was the realization that Catholicism was a strong foundation on which to build a healthy environment in which to raise well-adjusted, moral, and happy children. All of my children, and sons and daughters-in-law are devout, non-judgmental Catholics. We have 22 grandchildren all of whom have been raised Catholic. Four of them are now married and have given us three great grandchildren. My wife and I are now responsible for bringing 37 Catholics into the world, with many more to come.
Happy New Year
Yppop