Does Chopin’s characterization of Mrs. Mallard in "The Story of an Hour" justify the story’s unexpected and ironic climax? Explain your response.

This would, at least in part, be a matter of opinion, and
opinions could easily differ. 

If Chopin has a weakness,
it's that she's a bit didactic, or preachy.  She has an agenda when she writes fiction. 
An agenda is entirely appropriate for an essay, but not usually for fiction. 
Sophisticated fiction usually raises difficult questions and doesn't pretend to have
easy answers.  Chopin somewhat avoids this, however, by making the husband blameless, or
mostly blameless.  Her husband seems to be a good man and treats her well.  Chopin's
problem is with the institution of marriage in a male-dominated society.  She is not
husband bashing, in other words.

The question of the
surprise ending, as it relates to Mrs. Mallard, deals mainly with two details revealed
earlier in the story:  her heart condition and her excitement over being
free. 

First, because she has a serious heart condition, a
heart attack is not out of a question and is causal--there's a cause, it seems fairly
legitimate.  Others in the story worry about her having a heart attack when she finds
out her husband is dead, so it is a legitimate concern.

Her
excitement is also clearly established.  She is ecstatic.  Though the story is even
shorter than the "hour" of the title, her feelings of freedom are thoroughly
established.

Thus, her heart condition and excitement would
seem to make her fatal attack when her freedom is taken away unexpectedly
legitimate.

Another issue is whether or not her husband not
being in the accident and arriving at the home is legitimate.  But that is another
issue, and you asked only about the characterization of Mrs.
Mallard.