What do you mean, their own style? Are you referring to how the characters in Sam and Max, Tales of Monkey Island, and (from what little we've seen of it) Back to the Future all have this vaguely similar look?
That could be neat, but the reason why the South Park character creator works is because South Park uses an extremely simple style. Most characters are identical to each other save for different hair and clothing. With Telltale, that's something a little trickier.