If address A sends address C a transaction with a low fee, B can use CPFP to receive the funds quicker.
I assume you mean if address A sends coins to address B, then yes, B can use CPFP.
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?
Yes, provided C has paid a high enough fee to bump the overall fee rate for both unconfirmed parents.
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?
No, not correct.
Miners will consider the transactions as a package. It doesn't matter too much if the package of transaction is a chain of two unconfirmed transactions as in your first example, or if it is a chain of three unconfirmed transactions in your second example. Miners will look at the total space taken up by all the unconfirmed transactions in the chain, the total fee paid by all the unconfirmed transactions in the chain, and then work out the effective fee rate and whether or not it is worth including the entire package of transactions.
So yes, C can use CPFP, but will need to pay a fee high enough not just to bump the B to C transaction, but also to bump the A to B transaction.