Yes, the Kurds would be cool if the United States withdrew from Iraq, because they already have a great deal of freedom. The Kurds have regional government in a separate location, and they already enjoy a great deal of autonomy. They would not want to upset this balance just to have official independence.
Yes, withdrawing from Iraq, the Kurds would likely maintain stability in the area, and would not seek to establish Kurdistan. The Kurds have witnessed terrible conflict in past years, and currently enjoy relative autonomy, with regional government. After the U.S. Invasion, the Kurds have been hesitant to send troops into Baghdad, which is a sign that they will likely continue to enjoy relative isolationism in favor of peace, rather than conflict.