No. The Nazi Party (NSDAP) used "National Socialist" in its name for populist appeal to workers in the 1920s, but it rejected Marxist socialism, class struggle, and internationalism.
They purged their own left-leaning "socialist" faction (Strasserites) in 1934's Night of the Long Knives, banned socialist/communist parties, sent their members to camps, allied with big business, and ran a fascist mixed economy with private property under strict state control for nationalism and war prep—not worker ownership or equality.
It was fascism, not socialism.