When you pitch the yeast - If there is Oxygen available , yeast will use it to respire (use Oxygen to produce ATP) while consuming the sugars in the wort, and not produce Alcohol. Once the available Oxygen is gone, yeast will revert to fermentation to produce ATP while consuming the sugars in the wort.
There is no chance Oxygen will be left over, unless some is in the head space, or introduced when racking.
As for how much Oxygen to add when pitching, many home brewers splash the wort/shake the bucket etc with good results. For higher gravity beers you may want to Oxygenate the wort.
Actually, due to the Crabtree Effect, both take place simultaneously. Crabtree says that in the presences of a >.5% glucose solution, fermentation will begin immediately.