Almost always. CwD is generally a prevent, because an ongoing negate that is already on the table is a prevent, and it would prevent CBI abilities. However it is possible (with Meal in Emmaus) to activate CwD after a CBI character's ability has gone off, and if that happens CwD can't stop the CBI character's ability.
Cannot be Prevented cannot be stopped before the fact
Cannot be Interrupted cannot be stopped after the fact
Cannot be Negated cannot ever be stopped.
