The Chlorella will not help you to cleanse faster while fasting. It shouldn't affect ketosis. However, while fasting you should not consume anything aside from pure, clean water. Any vitamins etc. will 'fool' the body into thinking it's still eating and as such it will continue to burn it's own nutritional reserves more freely.
When only water is taken, those reserves will be preserved for as long as possible to stave off starvation.