Exactly – Both of those abilities work in full, because hits and mast eliminations are separate things that may or may not trigger other effects depending on their specific wording.
If you also throw in the ability that eliminates two masts with a single hit, you end up with a sequence something like this:
First Hit – Eliminates a crew, but no mast damage.
Second Hit – Eliminates two masts.
Third Hit – No damage.
Fourth Hit – Eliminates two masts.
Fifth Hit – Etc. (alternating)
A ship like Asesino de la Nave (or La Belle Etoile) will still destroy cargo with every single hit, even if only every second hit eliminates a mast on the target.