Can fermentation and aerobic respiration occur at the same time?

In muscle cells during exercise, does lactic acid fermentation and aeorobic respiration occur at the same time, and does this mean the cell makes more or less ATP during this time?

The cell can’t completely lack oxygen, which means that some of pyruvate will move into the mitochondrion, however, lactic acid is also produced which means that anaerobic respiration occurs. Is this reasoning correct or is there some other mechanism that I am skipping that doesn’t allow these processes to simultaneously occur?

Also, the NAD+ used for glycolysis is regenerated and net 2 ATP is releaseD in glycolysis, but the NADH doesn’t move into the mitochondrion, so if pyruvate moves into the mitochondrion at the end of glycolysis, then there will be less NADH in the mitochondrion, which makes sense because there is too little oxygen and too many electrons in the ETC.