Personally, I'm not a fan because juicing concentrates a lot of sugar into one drink and removes all the healthy fiber from the veggies. Sugar in any form causes fibro flares for me. Vegetables are very hard for me to digest anyway, and they cause IBS in me. Removing the fiber would mean I wouldn't digest much of the vegetables, because the fiber is what causes a slower healthier digestion. If I don't digest slowly, I don't really absorb any part of the food, except for some of the sugar because it is the easiest, fastest nutrient to absorb. To me, it sounds like an invitation for a fibro flare in the same way eatinghalf a dark chocolate bar invites fibro.
The only vegetables my doctor let's me eat are ones that are easy to breakdown with the least amount of starch and sugar: asparagus, green beans, spinach, kale, artichokes, and cucumbers. I can have cabbage and broccoli in small doses if they have been cooked down in a crock pot for several hours, but raw they reap havok on my gut!
So I would be careful. There are other methods of detoxing that get more nutrients into you than juicing.