No.
The New York Giants were in the National League.
American League
The new York Yankees and the Los Angeles Angels both are members of the American League in Major League Baseball, though the Yankees are part of the American League East and the Angels are part of the American League West.
The Yankees have won 40 American League pennants.
The Yankees have won 40 American League pennants.
Yankees American League
The New York Yankees beat the Boston Red Sox in the 2003 American League Championship Series.
No. The Boston Red Sox are an American League team as are the Yankees. The World Series is played between the American League, and the National League.
American League (East division)
The Yankees played in 43 American League Championship Series and won 40 pennants.
The Yankees played in 43 American League Championship Series and won 40 pennants.
No Yankees player has ever won the National League batting championship as the Yankees play in the American League.