I bought a dell Inspiron i5 7000 7567 gaming. It has 8Gb DDR4-2400 ram. I was going to add another 8Gb of DDR4-2400 (~$90) but was wondering if there would be any real world difference in speed if I went to a 2x8Gb DDR4-2800 (~$180).
Does the i5 7567 have a physical 2400 limit?
My gut says I won't notice any difference.
No, you won't see any improvement by going for DDR4-2800. From a gaming perspective, I don't think you'll see an improvement going from 8GB to 16GB with that configuration. There are plenty of Windows programs that can chew through RAM though so 16GB may still be worth it (depending on your use).