No.
Glycolysis doesn't need oxygen to produce ATP.
Aerobic respiration (i.e. through electron transport chain in mitochondria) needs oxygen.
Duke: the products of glycolysis CAN go into the oxidative cycle, or if there is no oxygen they will go into the lactic acid cycle, which creates lactic acid as a byproduct. So yes, glycolysis does produce ATP without oxygen, and yes it is far too inefficient to allow a human to live without O2, but you can get simple organisms like yeast to survive this way, for example.