CFS is caused by Leaky Gut as you might be aware and therefore fasting or limiting what you eat ie not taking protein or fat but taking important nutrients which contain no protein/fat or constituents that the immune system can react to should provide some help.
However this cannot go on indefinitely as the human body needs protein and other nutrients on a regular basis.
If you try it make sure that you get some magnesium which your body needs and will not cause an immune system reaction. Vitamin C and B vitamins providing you have a source which does not contain allergenic compounds. Powdered sources without any fillers or additions such as rice powder or anything like that might be okay.
In theory it should provide some small benefit and maybe allow you to know what it is like to be without CFS, but it cannot go on long!