Will a DDR3 2133Mhz improve the integrated graphics of a A6-7400K

Solution
yes faster RAM will produce the best results if using the onboard graphics of an APU. Please note this only works if you only use the faster RAM, if you keep your old RAM in the system the RAM will only run as fast as the weakest RAM.
For gaming quality, I'm pretty sure that neither the GPU or on-die graphics would help much. But if you want to expand, I'm sure you could tell your BIOS to feed it more RAM. Check your motherboard to see the max suported frequency too, by the way might not always be the max.