No. The only Super Bowl teams to appear in three or more consecutive Super Bowls were the Miami Dolphins (Super Bowls VI, VII and VIII) and the Buffalo Bills (Super Bowls XXV, XXVI, XXVII and XXVIII).
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The Cowboys won back to back Super Bowls in 1993 and 1994 (Super Bowls XXVII and XXVIII).
No, the Pittsburgh Steelers are the only NFL team to have won 6 Super Bowls and they did not win them in a row.