I think the flush recipe calls for fluids only during the flush (and nothing at all from 2 PM till 6 when you start).
I recall the instructions for the oil/juice mix say to remove the pulp with a fork. Besides, a lot of folks get nauseous from the ES and oil/juice mix so the less solid stuff in your belly the better.
So I'd say (and this is just me) use the juicer and strain out the pulp.