I think it depends on how much olive oil you put into the drink. if you dont put too much it will be okay I think. If you put too much (more then a table spoon) then it might hamper your digestion at lunch time and the foods you eat during the day will not be digested properly. So adjust the amount of olive oil so you are hungry when your next meal is to be eaten :-) i would keep on doing it until you dont feel like it anymore. Listen to your body. It will tell you when it had enough of this kind of breakfast.
An alternative great drink to tone the liver I have posted under diet a few messages below. But I put only a teaspoon of olive oil in it and one can drink it as breakfast or on empty stomach before drifting off to sleep