The events in the books take place _before_ the game, so no - it's possible to read all books and then play the game, which (in that case) is a continuation of Geralt's story. It's pretty awesome actually.
I played the game long before I started reading the books (I had never heard of the Witcher) and it happens (in the game) that Geralt runs into certain characters and they act like they know him and I wasn't sure what to think of it then. Since I didn't know them, they could have been lying or whatever, but someone who has read the books, knows they are indeed telling the truth. Also, there will be certain dialogs, when a situation from the books is referred to. So having read the books is the difference if you'll know all about it, or if it's just meaningless to you/a phrase like any other.
But in general the game is really made so it's not necessary to know the books at all, it's usually just references that will make someone smile every now and then, if the player knows more about it.
The books basically created the world, the game takes place in. So every reader of the books will be accustomed to this world already, when starting to play the game. I like that. They are like an encyclopedia for the game. The books prove that CD Projekt did a really great job at building a game from these stories about Geralt, that already existed.
I'm currently trying to read all the books before The Witcher 2 comes out in May (I started the third book today). I like them a lot so far! I speak german and in that language only 1 book hasn't been released yet. The last one will come out in March, long before I will have read the first 6 books, so soon enough for me.