The experience of esomnemism would be identical to the experience of using stored memories. The only way to determine if esomnemism is true is by understanding the physiology of the brain, specifically the parts involved in memory.
If esomnemism is true, it obviously isn't perfect. We cannot see the past clearly: we forget things. This may be because 1) our "vision" into the past is not 20/20, it is flawed; 2) we can only "see" things that we actually witnessed at the time; 3) because of multipathism, there are many possible pasts.
Esomnemism, though perhaps true in itself, is also very useful in arguing multimnemism.
Esomnemism, if true, may rely upon quamepsychism, which states there is a neural interface to the quantum world.
Evidence for esomnemism
1. Studies have shown that the parts of the brain responsible for recalling memories are the same parts that are responsible for the observation. For example, recalling a visual scene utilizes the visual cortex.
2. The shear volume of memories that a person has access to is amazing. It seems like a lot of information for a "mere" 100 billion neurons. If those memories are not actually stored in the brain, it frees up a lot of room.
Evidence against
1. There is no correlation that I know of between amnesia and blindness. This fact weakens a possible link between memory and the senses.