Assume that all payments are RBF enabled.

If address A sends address C a transaction with a low fee, B can use CPFP to receive the funds quicker.

If address A sends address B a transaction with a low fee, and then B sends it to C, and then C uses CPFP to increase the fee, will the transaction actually confirm faster? I thought not, because the CPFP would only apply to the B to C transaction, and not touch the A to B transaction. Is this correct?