yes, adding the live rock is what will accelerate the cycle. The micro organisms in the rock will migrate into the sand and flourish. That creates the beneficial bacteria that help break down nitrates and the nitrification cycle. If you were to not add live rock youd be looking at a 4-5 week cycle, the lr
will cut that time in half. If it is uncured then the die-off will restart your cycle but not by much because of the ammonia released from the dying of organisms and plants.