The enters-the-battlefield effect of Archon of Valor’s Reach is a replacement effect that doesn’t use the stack. No player can cast spells or activate abilities after it has entered the battlefield but before you choose a card type.

Whether it’s legal to cast a spell is determined before its costs are paid. This means that if Archon of Valor’s Reach has sorcery as the chosen type, you can’t cast Morbid Curiosity, even if you wish to sacrifice Archon of Valor’s Reach to do so.