Barely something imo... The problem with AAA third parties and Nintendo is not the hardware performance, it's the audience, that's why you'll keep seeing JRPGs and Indies sell more on Nintendo than AAA even when they start releasing day one too.
Indies, JRPGs and other gameplay heave games are more in line with Nintendo audience tastes so COD or not, they could sell well but will still be behind PS/Xbox despite Switch or next Switch being the best selling console ever when they release them.
That said, COD and any online game is very gameplay focused so maybe there's a chance it shines there too.