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.
However, 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?
First of all, for the transaction to confirm faster, it depends on how mempool is congested with unconfirmed transactions and how much sats you are willing to replace the fee with, if you pay a high transaction fee for Child pay for Parent(CPFP), it will confirm faster( most likely in the immediate block) but if you pay low a fee, it will stay in the mempool until a miner pick it up; If RBF is enable, you can bump the fee.
In addition, the CPFP transaction is paying the transaction fees of A--->B and B--->C together, but how fast it becomes confirm depends on how you prioritised the fees.