Of course it can happen, and it is, I think, independent of trauma or not. You aren’t just four letters of a psychiatric acronym. When we’re working on ourselves this becomes so immense that it’s easy to us to loose the big picture of sight… people will love you because you are lovely, intelligent, creative, funny, put your good reasons here, and well, this always is bigger than "the person with issues". Sometimes the issues might make relationships fail, but it doesn’t prevent you to love, be loved and have your chance.
Plus, there are many many dingusses around that aren’t diagnosed with anything, but still are very awful. Not everything has to do with mental health. Now periods of being alone can be cool too. It doesn’t mean it has to stay that way forever.