The old zones are still there, just rearranged....
And yes, you would be able to see everything without Cataclysm, you just wont be able to play the new races/fly in Azeroth/advance to level 85/etc... when the expansion comes out on 7 Dec.
EDIT: By "base game and first expansion" you are still two expansions behind as you only get the main game and the "Burning Crusade" expansion. You would then need to buy the "Wrath of the Litch King" expansion and then the "Cataclysm" expansion if you wanted to be fully up to speed. With that in mind, I dont really know what you would or would not be able to see wrt the shattering.