Yes, it is a variant of mutual information. If P(X) = 2^{-K(X)}, and we use the maximally compressed form of C (denoted by C^*), then ASC(X,P,C) = K(X) - K(X|C^*) = I(X:C), where I(X:C) is algorithmic mutual information. Per our last discussion, algorithmic mutual information cannot be generated by random and computable processes any better than by flipping a coin. Hence my claim that naturalism cannot create information that fits our intuitive notion of information.
If you properly formulate P based on all possible chance and necessity causes, then yes, X with high ASC would give high probability something other than chance and necessity created X.