Do the Swing components support displaying international character sets?

Yes.

Assuming you have the proper font installed, the following will display Kanji characters for the Japanese numbers:

import javax.swing.*;
import java.awt.*;

public class TableSample {
  public static void main(String args[]) {
    Object rows[][] = {
      {"one",   "ichi - u4E00"},
      {"two",   "ni - u4E8C"},
      {"three", "san - u4E09"},
      {"four",  "shi - u56DB"},
      {"five",  "go - u4E94"},
      {"six",   "roku - u516D"},
      {"seven", "shichi - u4E03"},
      {"eight", "hachi - u516B"},
      {"nine",  "kyu - u4E5D"},
      {"ten",   "ju - u5341"}
    };
    Object headers[] = {"English", "Japanese"};
    JFrame frame = new JFrame("Sample");
    JTable table = new JTable(rows, headers);
    JScrollPane scrollPane = new JScrollPane(table);
    frame.getContentPane().add(scrollPane, BorderLayout.CENTER);
    frame.setSize(300, 150);
    frame.setVisible(true);
  }
}