Musician here. 4'33" is definitely music, and I even consider it one of the most important experimental pieces that exist.
In essence, anything that revolves around sound can be called music, if the artist wishes to call it that. Silence is part of music, although typical music doesn't only consist of silence. This piece makes people focus on the sound of silence for longer than their attention span is comfortable with, and elicits quite interesting reactions from the listeners that way. It's a great experiment, it has some subtle shock value, and it has led to countless philosophical discussions such as this very thread. I am pretty sure that if John Cage reflects on the success of this song and its experiment, he is very pleased with how it turned out.
tl;dr: yes.