When I did my first fruit juice cleanse, I was amazed at the results (I felt and looked better, etcl), I thought it made sense to give the digestive system a rest. I look at it as a kind of maintenance, similar to when we do oil changes on our vehicles.
To me, it seems that if our digestive system is cleaned out, it should help with bad breath. In simple terms, it's one long tube and if something is rotting inside, the smell will be noticeable.
Different things work for different people. For me, the one thing that has helped me the most is fruit juice fasting.
I think it's like anything else. If we do it and then go right back to our old habits, not much will change. It's when it's part of ongoing lifestyle changes that it will help the most, IMO.
One word of caution though: bad breath will temporarily get worse during fasting, while things are being eliminated. It gets worse before it gets better.