Yes...many people do the Liver Flush without parasite cleansing first (they may get to it afterwards). Some people feel fine without it, some people not. I know that my first parasite cleanse was GREAT and I just did it after 9 days of MCing. (no parasite cleanse) I think that Liver Flushing after fasting is excellent...I encourage you to do it!
Plus..you're already parasite cleansing! Right on.