Yes, typically a person with any level of appreciation for art (and i mean a person over the age of about 4) will be able to recognize intuitively which pieces have a certain degree of conceptual value behind them where others do not, even if they cannot grasp the depth of it. there are a number of levels that I've observed and there are probably many others:
instinctive : everyone from birth, even animals (and some people say, plants) are able to understand (if not articulate) the entire spectrum of aesthetic choices (in the pure sense of the word, i.e. how formal qualities create sensations and nothing more)
self-defined : at a very early age, children are able to relate complex emotions and connections via their own sense of things, although these connections will usually not make sense to anyone else as they are established within the child's psyche.
able to understand symbolism : strong
conformed : children of schooling age have recognized society and accepted its standards; the early understandings now merely an unexplainable feeling. things are often broken down into simple and somewhat permanent categories of good and bad.
able to understand symbolism : very weak
exploring within society : teenagers are exposed to a much broader and more contradicting world than they had ever anticipated, and they seek out answers from the world to define for them what is good and bad and how they should feel (this is true regardless of whether they are mainstream or a rebel, as rebels are defined by the mainstream anyhow, and also true regardless of whether they are a specific type, jock, geek, artist, et cetera, or if they take their identity buffet-style from those). this defines most "mental students" and is a necessary stage for social existence and in art technical understanding.
able to understand symbolism : contextual only
self-realization : at a certain point in one's life, they become aware that all of their emotions are within them and that the only thing stopping them is the habits and conditioning that came out of the previous stages. Most young people who have moved past a student mentality remain in this stage for any number of years. This is a necessary stage for establishing style, goals, and general confidence as an adult.
able to understand symbolism : contextually and as it relates to personal experience
universal realization : eventually, people realize that their mind is not the only mind aware of itself, and they are finally able to fully appreciate life, the universe, and everything. Many do not seem to reach this point; Michaelangelo, Picasso, Van Gogh, to name a few, and live their lives in a mixture of conceitedness or loneliness or both. Don't mistake me - there will always be a certain level of respect that anyone can muster, probably based on the idealizations ingrained by previous stages, but they will not necessarily have a spiritual relationship (in the non-religious sense) with the rest of the world in the same way that someone who becomes universally aware will.
able to understand symbolism : contextually, personally, hypothetically (all possible meanings), and sympathetically (what it might mean to the person, though this will always be a guess)
personally i don't know where I fall, probably somewhere between exploration and self realization. It's amazing how much my perception is still colored by the world around me instead of my own thoughts.
