The consensus is that you want the oil to draw impurities from the blood and that its ability to do that is hampered when there is food in the system.
That said, I often OP well into the morning -- after food, coffee, etc. -- and I still feel the amazing benefits. I am sure that I would see more were I to get out of bed and start swishing, but that remains a goal/ideal around here as my twins usually have completely different plans for me...
One thing I really appreciate about this protocol is its flexibility!
Good luck and happy pulling,