No, because all the characters are seen to be odd in some way. For example Joy is seen to be very rude and awkward and endowed with a monstrous intellect at the expense of feeling, and given to strange behaviour such as officially changing her name to Hulga, which leaves her mother quite at a loss. Mrs Freeman's main interest in life seems to be the discussion of other people's ailments, and so on. The more peculiar qualities of the characters are deliberately stressed, giving rise to a sense of the grotesque, and human relationships are portrayed in a strange, skewed manner. This is quite typical of Flannery O'Connor's writing. As a result it is not very easy to conceive much empathy with the characters; it is almost easier to laugh at them.
However, it is possible to feel sympathy for Joy by the end, after her appallingly callous treatment by the boy she had planned to run away with. She might even be regarded as admirable, albeit to a rather limited extent, in her highly individualistic manner of thinking and behaving. Also, in general, the characters in the story might be regarded with some sympathy for the extremely isolated existences they are seen to lead.