The answer to this question will depend, in part, on your definition of a good Christian woman. Were the definition charitable or forgiving, then the grandmother might well be described as a good Christian woman. She loves her family and strives to act according to what she believes is right.
However, the grandmother's sense of right is highly convenient and selfish. She is deceitful, arrogant, manipulative, bitter and judgmental. As a person who seems entirely to lack generosity of spirit and who ultimately disavows the Christian miracle of Christ raising the dead, the grandmother does not seem likely to fit most narrow definitions of a good Christian woman.
Early in the story, the grandmother demonstrates her negative traits. The text of the narrative overtly suggests that in telling her son, Bailey, that the family should go to Tennessee for their vacation instead of Florida she is attempting to manipulate her son. The family wants to go to Florida, but she wants to go to Tennessee. She does not admit this to be the reason she points to the newspaper story about the criminal/killer on the loose, the Misfit. Instead, she moralizes (with a quite false morality, as it were) and suggests that her son is putting his family in danger (and so he is being a bad parent).
She says that if she were headed to Florida where the Misfit was thought to be,
"I couldn't answer to my conscience if I did."
A question arises here, early on, as to the primary or principal irony of O'Connor's story.
- Is the irony that the grandmother claims to be a good Christian woman when she is not?
- Or is the irony that her manipulations and schemes, which lead to the deaths of every member of the family, are initially presented as a way to avoid being killed by a roving murderer?
Perhaps these two ironies are very similar in the end. Yet, the inflections of each differ. If the irony is oriented by character, we have to see the grandmother as a false person hiding behind piety, who ultimately is confronted by a man who is explicitly and decidedly against piety and religion.
This reading puts the grandmother's essential falseness at the center of the story and contributes to an overall theme of the difficulty of finding a good, truly faithful person in the modern world.
The second irony leans toward a broader statement on the folly of human intentions and allows us to read the character of the grandmother with less blame. She may be, in this reading, merely flawed - as all people are.
This reading easily incorporates the faults of the grandmother in terms of the cause of the car accident. It is her fault of memory that the family heads down the wrong road. It is her fault of honesty that leads her to bring the cat along on the trip (and the cat's release in the car then directly causes the accident). The deceit of the grandmother is thorough, though in some ways it is also simply childish.
"Her lie is selfish but by no means atrocious, yet the consequence for this lie is death, for herself and her entire family" (eNotes).
Seen in this light, the grandmother's character might be understood with some empathy. She is not the same kind of monster the Misfit is. Rather, her willingness to act selfishly and deceitfully are a quite pale comparison to his willingness to kill, rob and destroy. She wanted to get her way and so lied, almost innocently. Her false piety is, perhaps, similarly self-serving but also innocent and unenlightened.
Unlike the Misfit, the grandmother does not realize that she is not actually pious or "good." Like most people, she has a limited self-awareness and just happens to be superficial and haughty - flaws that might usually be forgivable.