Unfortunately no, chaining only affects wild encounters while the Masuda Method only affects eggs. However, if you’re willing to go through the trouble of completing the Pokédex in order to get the Shiny Charm, then the charm’s improved odds can stack with either chaining or MM.
Edit: misunderstood what you meant. I don’t see why you wouldn’t be able to do both at the same time, although it also depends on your target; if you’re hunting something with a low encounter rate, especially if it can only be found through shaking grass encounters, then I would recommend only trying to breed for it. Every battle you have with a Pokémon that’s not your target will just slow you down, so if you only have a 10% chance (or less) of encountering your target then it’s just not worth it. I’d say to only try doing both if the Pokémon you’re hunting has a slow hatch rate and can spawn in the overworld.