We had an interesting question arise in our Shul this past Yom Yerushalayim. Our shul has a minhag of saying Hallel without a brocho in Shacharis. At one of the minyanim, the chazzan said a brocho at the beginning of Hallel ("likro es ha'hallel"), out of habit. The question is, does the fact that he said a brocho at the beginning of hallel necessitate the recitation of the final brocho ("melech me'hulal ba'tishbachos") at the end? I don't have any reason to assume either way—I'm not even sure that the two brochos are related—but I'm still curious. Note: the fact that some hold a brocho should be said on Hallel on Yom Yerushalayim should be excluded from this analysis.
In Mishna Maseches Sukkah 3:11 it says that the after Beracha of Hallel is not obligatory like the first Beracha -so it's obvious that one would not say the after Beracha in the case of the question.