Appreciation is subjective, so only you can answer that. “Truly” is one of those “weasel” words that creates mischief in discussions. It opens the door to elitists who will disparage anyone below their level or specialty. I once had a pianist tell me that you you can’t truly appreciate Chopin unless you play the piano. A composer might respond that the pianist can’t appreciate Chopin because he is not a composer. All BS. No doubt stronger go players appreciate much more than weaker players, but that doesn’t mean there is no appreciation at lower levels. If there were not some appreciation, people would stop playing go. There is no “truly” about it. @spatula very nicely itemizes levels of increasing appreciation all along her go journey.
I would also caution against over-intellectualizing this question. One’s strength doesn’t depend only on one’s ability in an intellectual sense. Emotional factors affect all game play. This is most obvious in poker. In go, one’s personality can have a significant effect on how one plays; most obviously, at all levels some players are more aggressive than others.
Personally speaking, I have a pretty good idea of my weaknesses in a game even before the game ends, because one sees the results pretty quickly in most cases. A year ago, doing tsumego, I had the epiphany that it all involves dividing the space; one has to see how the space is divided to make two eyes. That was a gain of appreciation at about 18k. Reading the Forum 8 or 9 months ago, I learned the proper way to shut down a dragon, and just had occasion IRL to put it in practice. Another gain in appreciation. I’ve recently gained appreciation for the vital importance of sente and am struggling with the art of tenuki. The scattered, acrostic-style of play that you see among high dans and pros, however, is baffling. It obviously represents really long-range planning of an order beyond what I expect to ever understand, given my advanced age.