No. This case about citizenship for people born in American Samoa. Federal representation for people living in American Samoa is a separate question. American Samoa, like other U.S. territories, has limited federal representation because the U.S. Constitution only provides Presidential Electors to states and the District of Columbia, and voting representation in Congress has not been extended beyond the states.
If the case is successful, people born in American Samoa who already live in or who move to another part of the United States would be permitted to vote in state and federal elections there. Currently, every state denies the right to vote to people who are classified as “non-citizen nationals.”