First, it is important for mental and physical health to get enough sleep. On a juice fast you will not need to spend the time shopping and eating so will that give you more time to sleep more?
The juice fast with fruit and vegetables juices is a slower cleanse than water fasting or master cleanse lemonade fast so people have been able to do it without changing their daily routine. This site on Fasting has MDs saying that they could continue their daily routine during juice fasting under Juice Fasting. It has quotes from 17 different MDs.
Generally speaking, vegetable juices cleanse slower than the fruit juices. Of course like any fast that someone is doing on their own, you determine things by what happens day to day. So you can always break the fast if it is too much. Good luck!