Would plants grow via hydroponics in an atmosphere with no oxygen, if the water is continuously oxygenated? why?

"Growers using organic soils will never concern themselves with supplying oxygen to their plants; however, hydroponic growers like me must be well versed in the science of dissolved oxygen (from here on out called DO). While most crops seem to prefer about 9 PPM DO, some crops like lettuce have demonstrated little to no difference in fresh weight or dry weight when grown in DO levels ranging …"

Explanation: