As some of you already know, I am a fan of Adam/Laura. I think the story started to go one way and then when Adam decided to sign on again for another season, the writers had to (quickly) change the characters to make them fall apart.
Before that, the story was going forward with a young woman who was a mother and just lost her husband. She was not strong and she needed a lot of direction. I believe that (at the time) that's what Adam wanted, a young women he could grow with and she would always admire him for his strength and his smarts.
OK, now that I said that ... back to the question.
What would Adam do if he found out after they were already married. I think he would confront her and if she was willing to make a go of the marriage and move forward being a loving wife to him, then I think he would let the past be the past. I'm saying this because it was 1865 and things were not the same as they are today. I don't think people got divorced easily and then there was Peggy. I doubt Adam would give up on a family that easily. I do think couple married for different reasons and couple grew to love each other. In this case, I think it would be easy. I mean, neither of them are hard to look at.