Logically, they would have wanted to have killed him. If Zazu got away alive , even if they had managed to kill Simba and Nala, guess which three suspects would have been in deep doo doo with the Pride had he gone and told Mufasa who attacked the cubs.
Mufasa might have let them off with a warning that he'd kill them if they ever tried to harm his son again because Simba and Nala lived, but if they hadn't, I think it's a safe bet that Mufasa would have sicced the lionesses on Shenzi, Banzai, and Ed for the deed and killed them.
Also, when we see Mufasa arrive, he is with Zazu. Also, i think in Lion King 1 1/2, Zazu actually was sending Mufasa to the Elephant Graveyard to go save the cubs (unless I'm thinking of the "Look sire, they're bowing!" scene instead.)
Had the trio whacked Zazu, they likely could have killed Simba and Nala too and gotten away with it.
Thankfully, they seemed to be too stupid to realize this.