Not being educated on the subject, I cannot argue the point, but I think it is a stretch to say that you derive any nutrional value from OP.
If I understand it correctly, it has a drawing effect from the swishing the oil in the mouth which traps the bacteria in the oil. It is not swallowed, and your mouth is then cleaned by brushing, and rinsing.
If anything, it would seem to be a bonus to fasting in that it eliminates (detoxes) muck before it has a chance to go through the normal channels of elimination deep in the body.
Also since it doesn't get to the stomach, and digestive system, it would have no effect on fasting since it would not take energy away from the body detox that is the purpose of fasting.