With Tingalf dead you may miss a bit of experience for parts of the quest (see the link Macbeth posted). You at least need him alive to get a clue to the location of the black market goods (after you follow up on the missing wagon), but you should be able to do much of the quest.
For the rest of the game it will not matter if he is dead. Completing the quest would result in him being arrested and taken away, anyway.
