Characteristically, becoming the leader of a foreign country would require relinquishment of American citizenship. Even if that is not formally required by the foreign country, taking an oath of office and loyalty to become a foreign leader or other foreign public official is usually considered to be an act that is inconsistent with holding American citizenship and to work as an automatic rejection of it.
Maybe, unless the person specifically stated they were not renouncing their American citizenship, kept their passport, paid taxes, etc.
It is the sort of thing that would need to be tested in court.
However it is really hard (justifiably so) for a natural born American to lose their citizenship. Even renouncing it voluntarily is difficult.