Red Question, the - Crimeth INC

Name: The Red Question
[AU:C]
Cardtype: Action Modifier
Cost: 1 blood
Burn Option
Requires a non-titled, non-Anarch vampire.
Put this card on this vampire. This vampire is considered Anarch. Burn this card if this vampire changes sect.
Artist: Carmen Cornet

Name: CrimethInc.
[TR:C]
Cardtype: Action Modifier
Discipline: Protean/Quietus/Thaumaturgy
Requires an anarch. Play after resolving a successful action that requires an anarch or makes this vampire an anarch.
[pro] Unlock this anarch.
[qui] Unlock another ready anarch.
[tha] Put this card in play. During your minion phase, you may burn a pool to unlock a ready anarch you control.
Artist: John Bridges

Is it correct to assume that ANY successful action in which the Red Question is placed on a vampire makes they anarch, and then they can play Crimeth Inc?

No. The action is neither an action that requires an Anarch (it couldn't be as they were not an Anarch at the start of the action), nor is it an action that makes a vampire an Anarch. Becoming Anarch via The Red Question is simply a side-effect of the action, not its purpose.