Probably Relic part would have a speed run but the gear chest won't. At the moment there is no point in looking at the relic quest walkthough since is going to change. 1.0 quest had hamelet seals, beast camp boss and coins, double meld weapon, 17 min runs AV and CC dungeon, weapon bonding, Ifrit Hard Mode and Garuda Hard Mode.
Thing confirm by Yoshi-P that will change in ARR.
Hamlet will be done different.
No timers for dungeons in ARR.
Dungeons will be labyrinths to different bosses for specific gear.
I imagen the sequence of items need it for Relic will stay the same, but the way to optain them will be different.