You do NOT have to complete this sidequest in order to get 100%. You don't even have to attempt to, but if you attempt all of the towers and talk to the Al Bhed guy at the travel agency, you get the Samurai's Honor Garment Grid.

Also, if you're about to go into chapter 4, with 46%, you're kinda behind. Have you visited all of the other areas in chapter 3 already?