It wouldn’t. It would drop the lesser gear score version of the BIS piece. Need to do level 15 to get the highest gear score version. Below is a chart of the gearscore drops you will get from the dungeon at different key levels.
The great vault side is the weekly chest gear score you will get. The weekly chest is like a bonus. Every Tuesday after server reset you get a box you open and can select a piece of gear. There is up to 9 choices you can select one piece. 3 choices from doing dungeons, 3 choices from doing raids, 3 choices from doing PVP. No matter how many choices you get you can take just one piece of loot though.
Notice that you only get ilvl 262 from a +15 as an actual drop. That is like heroic raid level loot which is still very good. In the weekly chest you would get 278 which is Mythic raid level loot (best you can possibly get.)
There are also other things you can get too. Like they drop mounts in dungeons. Also for timing all the +15 dungeons (there are 9 of them) you get a special mount as a reward and an achievement.
It still takes time to get all the best gear but at least you feel rewarded for your time even if you don’t get something every single dungeon which would be silly because you can infinitely spam them.
I believe there is also something now where if you are not good enough to do a +15, and they aren’t really that hard if you have some skill, you can take the piece you have from say a lvl 5 and upgrade it… kind of like the umbral shards here. Im not entirely sure how that works because I stopped playing WoW for NW before that part came out.
