Not necessarily a bad idea, but you don't want to go into a Liver Flush with nothing in your system but a few days of juice. Many of us don't eat the actual day of the flush, but you should eat on the days before that. Just avoid fats and heavy proteins. By eating, you "prime" your liver and gall bladder, and by avoiding fats it remains primed without releasing. Then, when you flood your system with the oil and juice the evening of the flush, bile is ejected with enough force to move stones, sludge, and cholesterol.
In my experience, a Liver Flush takes a lot out of you. I wouldn't want to go into one after not having anything to eat but juice for several days.
The idea of using malic acid, which apple juice contains and which tart cherry juice contains a lot more of, originated with Andreas Moritz . He claimed it softened stones, especially any calcified ones. But he said you needed a week or so of it to do any good. So while a couple of days of apple juice wouldn't hurt anything, it might not be enough to help much.
I have done about twenty flushes, and have alternated between using juice with malic acid and just skipping it, and except for the first two or three flushes, have not noticed much difference in results.