To a very large degree our brains are evolutionary equipped to analyze everything in our environment that presented before us (colours, people, noises etc) and subsequent to that there is a form of higher order analysis, where only the relevant information getting into consciousness. If you search for theories of attention you will see several views relating to this process, some processing different methods of course. The way in which we can prove (to an extent) some of these mechanisms is through experiments such as the cocktail and through monitoring brain regions when more than one sensory input are presented to individuals
Nevertheless, the evolutionary significance of such a system is very important. We are subconsciously always evaluating our surrounding searching for the slightest sight of danger, and if that danger comes then our limbic system is preprogrammed to take over immediately (e.g. loud explosion results in fight or flight response).
But the question is do we neurologically store all the information we take in? I think no, but what I will say is that studies of memory tell us that sometimes information is in memory but the inaccessible is due deficient retrieval. I am relatively sure that there is a memory theory called the "decay" one and that proposes that after a while information we possess disintegrates unless rehearsed. In addition, studies of STM show that it only has a very short life span.
You said that hypnosis could be used as a tool to test such a theory; I would have to disagree as it is prone to encourage individual’s false accounts in cases of uncertainty.
Kev