Doesn't look like it. After taking and completing this quest, I ran Azuchi lower dungeon several times. I did not notice any changes on any of the floors or the loot, and I still needed the key item
Tempyo Japanese Incense on me to gain access it.
Based on the dialogue in the quest, the fact you needed to have completed one successful run of Azuchi Mid to spawn this, and that the Japanese nation (and its dungeon Azuchi) came out first in Japan before the other EA nations opened up, I believe this was originally intended to unlock Azuchi lower rather then having a key item. This was obviously scrapped sometime during production in favor of the latter, like in Luxor. For whatever reason, KOEI kept the quest rather then removing it altogether (maybe it would have been too much of a hassle?). This is the only thing I can think of.
In short: It seems this quest serves no purpose at all. The only reason you would be taking this is either completion purposes, or you just want it to stop showing up at the guild in favor of a more useful quest.