No. He was nominated three times for Best Actor for three different movies. His Going My Way (1944) co-star Barry Fitzgerald was nominated for Best Actor and Best Supporting Actor for the movie....
Oscar Hammerstein II won Academy Awards for Best Original Song for "The Last Time I Saw Paris" from "Lady Be Good" (1941) and "It Might As Well Be Spring" from "State Fair" (1945).
The only Oscar to win an Oscar was lyricist Oscar Hammerstein II. The Irish writer and poet Oscar Wilde died in 1900, almost 29 years before the first Oscars were ever handed out.