Is it possible for a person who cannot trust anyone to have intimate relationships?

Can a person who is incapable of trusting others ever have a successful relationship? In the scenario I am thinking about, the non-trusting person has not had their trust betrayed by their partner, but their life experience has taught them not to trust people. I was thinking about kids with reactive attachment disorder who never had a loving adult to take care them as children and as a result never had a strong bond they could trust. Can these children grow up and have a successful relationship or is the ability to trust essential in every relationship? Do you think an adult can learn to trust?