No. eSRAM is used to make up for slower main memory.
Now as to why MS went with slower main memory: MS from the start wanted 8GB of RAM in order to accommodate their vision of having a box multitasking so many different apps/services. When they were planning their console, it looked like DDR3 was the only way to guarantee 8GB at a reasonable price.
Sony went with GDDR5 as the main system memory since they knew it would perform better for gaming and they didn't think they needed 8GB. Later in the dev cycle they were able to get 8GB of GDDR5 at an affordable cost so they upped their spec.
Thus is the story of GDDR5, DDR3, and eSRAM as it relates to this gen. (If I'm wrong or grossly oversimplified things, I am sorry).
Thank you, I never had a clear picture of the eSRAM situation until this thread.