To first answer your questions..
As a beginner could I recognize chords in music?
A: I probably could, but did I? It was a long time ago, but I'm pretty sure the answer is no I did not. I played the notes.
Should you recognize them?
A: The answer is most definitely YES!
I agree with the previous poster, many people learn to play without much theory, and I do think it's a detriment. I am 58, and re-dedicating myself to the piano after playing for fun off and on with some long (15 year) breaks. I got to a point of relearning and hit a wall, and then sought out an instructor. She has an advanced degree in music theory from a conservatory in Lithuania and she has opened my eyes to the importance of understanding theory. Theory is not just about knowing scales and chords and intervals, it's knowing how they work and understanding how the music is constructed. You play better understanding theory. You understand the progressions, you know what the music is striving toward, and you know when it gets there. That changes how you play it, you don't just play the notes willy-nilly. When you really really recognize where you are in the music, where you are going, and the path you are taking to get there, it allows you to bring out everything in the music.