I haven't read the Walking Dead comics yet. Would playing the games by Telltale give away much, or do they have a different storyline?
It is a completley new storyline. You can read from this link-
"...a game spanning five monthly episodes that tells a new story in the Walking Dead universe while staying true to the grim tone of the comic books."
Also, if you haven't read the comics yet, you really should they are amazing. The show is really good too, but it doesn't follow the comics all that well so far.
No, it will not. Each of the different "media" structures are different storylines.
TV Series - Is it's own storyline, surrounding a specific group of people.
Walking Dead - Telltale Games - Again a specific group of people, and it has no relation to the TV series.
Comics - Again, another entirely different set of people, with no bearing on either other form of media.
Then there are some other games (first person shooters, and so forth) and again for the most part, they are related to different random people.
Everything (from what I can tell) all take place in the same "world" but they are all different stories involving different people.