Would Sangan's effect go off if I detached him to activate Leviathan Dragon's effect?

Nope because he isnt technically on the field, when you XYZ summon something the creatures used as materials become a part of the XYZ. You will not get the effect.

When you overlay for a monster the materials become ....." energy".... for that monster. So to put it in a simple way....sangan effect turns into if you detach this unit from this monster this monster gains 500 attack. Its effect can't be used when it hits the grave because it no longer has an effect unless of course you put it back in ur hand and summon it then get it destroyed sacrificed sent to the grave tributed through card effect so on. that one card the bus guide I think is the only card that can use it's effect after it hits the graveyard because it targets a card in the graveyard and it starts a new chain.