The moral/immoral question was brought to the fore by Ms. Park's arrest. Without the arrest and and the subsequent public rebuke of the laws that required her arrest, the civil rights movement would have been deprived of one of its primary sparks.
In a country run under the rule of law, the law must apply equally to everyone. The fact that we had laws that did not apply equally to everyone was ultimately the undoing of and unfair system, but that system had to be legally unwound. Therefore, the laws that created the Jim Crow system had to be challenged and the people had to endure the penalties that were in place at the time for those unlawful acts. I don't know what sort of sense you are using the the word "deserve" in. I can only answer you that if you break the law, you deserve the penalty for breaking that law. Whether that law is a proper law or not is another question. (And, a mitigating circumstance to be argued in the penalty phase). But, clearly, you lose the moral component of civil disobedience if there is no penalty to be endured by the "disobedient."
As far as the summation goes, I'll give you the old lawyer saw:
"If the facts are on your side, argue the facts. If the facts aren't on your side, argue the law. If neither the facts nor the law are on your side, argue the Constitution. If none of those are on your side, ARGUE LIKE HELL"
Make what you will of that.
