Does Mary's pregnancy have influence on the story?

Mary's pregnancy has an effect on the story in a number of ways. It naturally makes her a more sympathetic character, so the reader can continue to identify with her even after she commits a brutal murder. The fact that she is expecting the baby in a few more months makes her completely dependent on her husband Patrick emotionally, financially, and in every other way. Thus her reaction to his totally unexpected announcement that he is leaving her comes as a terrible shock and makes it more plausible that she should succumb to a sudden impulse to kill him with the frozen leg of lamb she just happens to be holding. Furthermore, her instinct to get away with her crime is more understandable in view of the fact that she wants to keep her baby. If she went to prison, the baby would be taken away from her and she would never see it again. Mary remains a sympathetic figure because she is thinking about her unborn child rather than about herself. After the murder:

It was extraordinary, now, how clear her mind became all of a sudden. She began thinking very fast. As the wife of a detective, she knew quite well what the penalty would be. That was fine. It made no difference to her. In fact, it would be a relief. On the other hand, what about the child? What were the laws about murderers with unborn children? Did they kill them both-mother and child? Or did they wait until the tenth month? What did they do?

The fact that Patrick decides to walk out on his wife when she is six-months pregnant reflects unfavorably on him. It makes Mary's enraged reaction more plausible and induces the reader to overlook the fact that Mary is technically guilty of something like aggravated manslaughter. Most readers want to see Mary get away with her crime because she is the innocent victim of gross injustice.

Would Mary have killed Patrick if she had not been pregnant? Probably not. She would have lacked the last elements of outrage that gave her the strength and motivation to wield the weapon.

At that point, Mary Maloney simply walked up behind him and without any pause she swung the big frozen leg of lamb high in the air and brought it down as hard as she could on the back of his head.