The real benefit of an oil separator is the lack of catch can.
A traditional catch can system traps the oil that's suspended in your PCV system in a large can, forcing you to drain it and throw it away.
An air oil separator pulls the oil out of the air in your PCV system then drains it back into your crankcase. No need to ever drain it and no loss of oil.
When you are driving normally, oil begins to accumulate and circulate through the PCV system. When you nail the gas and the turbo spools up, a large amount of oil is pulled into the cylinder and burned. What we are trying to prevent is the oil being pulled into the cylinder, thus lowering the effective octane once it mixes with the fuel inside.