This question (and its sister) may be based on the way Arkham Horror expansions worked, in which the story of The Dunwich Horror or The King in Yellow was found throughout all the cards and monsters of that expansion. Eldritch Horror takes a different approach - each Great Old One has its own decks, and almost everything related directly to that story is in those decks. If you use a GOO from the core set, like Cthulhu, you will have a Cthulhu game no matter what other monsters/cards from other sets are included. The only thing you might want to be careful about are the Preludes that open up the Antarctica and Pyramid Sideboards - exclude those preludes if you don't feel like using those boards. Other than that, nothing will stop the GOO of the session from dominating the game.