The game will definitely have more impact if the player finishes COD: World At War sooner, mainly because of the story's plot. In the past I should have played the campaign to the end on the Xbox 360, it would definitely be one of my favorite games of all time, or rather, now it is.
When you finish the campaign, perhaps as a form of WAW Callback (because after finishing the WAW campaign you are directed to and unlock Nazi Zombies by playing on the first map "Natch der Untoten"), it starts Zombies mode on Map "Five".