I don't know. However, I do know that multi-cell pathogens such as you mention usually destroy tissue in their host, and CS speeds tissue healing in the human body.
That's a great question you're asking, BTW.
So in my opinion CS would help the body recover more quickly from the destruction they cause, and in my opinion you'd have to be using something else to get rid of the actual parasites, unless the body's terrain can recover enough health because of taking the CS to throw them out.
I know this is not an answer for you, but it's all I can be sure is true from what I do know.
I've been making and using CS for about 16+ years or so now..