I don't know based on the rulebook.

The provided rulebook context describes the requirements and effects of the Bloodletting Action (see page 26), including that a Cultist must be adjacent to an Investigator and that it increases the Blood track and gives a Wound. However, the context does not specify whether performing Bloodletting causes a Hidden Cultist to become Revealed, nor does it state that Bloodletting can only be performed while Revealed.

Additionally, the rules for becoming Revealed (see page 26) only mention that a figure is placed on the main board and their Revealed card is flipped face-up when they are Revealed, but do not specify which actions (if any) trigger this state change.

To answer this question definitively, the rulebook would need to explicitly state whether Bloodletting causes a Cultist to be Revealed or if it can be performed while Hidden. This information is not present in the provided context.

Source: Core Rules (pp. 22, 26, 27)