Interesting question, I honestly don't know. I did google it and from what I could gather it doesn't so much affect the white blood count as that the white blood cells become less useful as immunity hence why ms is known as an auto-immune disease (though I find the term auto-immune a bit oxymoronic as it sounds like we should automatically be immune to anything!)

after being on tysabri i have raised lymphcytes (not sure i've spelt that correctly!) which is a common occurrence and i think they are connected with the white blood cells - been told its nothing to worry about and they're just gonna keep an eye on it - pre-tysabri i don't know what my white blood cell count was x