I've never officially done a cleanse, but I do a form of intermittent fasting so I can attest that giving your GI a break will
absolutely help with the tummy issues. (I have gotten rid of my IBS this way!) I've read very positive things about juice cleanses for that reason.
Here's a really interesting an honest perspective on a juice cleanse from one of my favorite bloggers,
Dooce. She doesn't talk about the intestinal affects at all, but considering juice is removed of most of the fiber, it goes through the system really easily (unlike a smoothie where you wouldn't actually be giving your GI a break at all). Just make sure you have a good plan set up following the cleanse so that you don't go off the rails and wreak havoc on your system again.
Of course I would personally suggest fasting, but for me it's a lifestyle (I follow 5:2) not a one-off thing so I'm not sure how you would incorporate that into what you're trying to do short-term.