Once again, yes and no, in my opinion. From a classical music perspective, being a great musician is like being a great gymnast. You learn routines, which are performed as well as possible. All sorts of considerations are relevant in judging who is great, but essentially people are sizing each other up and comparing each other, to see who is the best.
This is also notably relevant in the jazz scene, where there is a grand pecking order or “food chain” that each musician tries to work his or her way up.
Additionally, from a commercial point of view, music can be about promoting self. You perform and promote in order to sell products and remain viable.
However I think it’s just too big a statement to say that being a great musician is essentially about promoting self. Music is first and foremost a form of art. We can and do use it as a communication vehicle, but this is primarily because of the way it appeals to the human soul at a deep level.
A person who engages deeply and powerfully with art is not necessarily promoting him or herself. In a true unfallen (or redeemed) sense, people may be rejoicing in and praising the creator! That is of course what art is meant to do: display the beauty of God. Music is not just a means to an end, where it is either exploited for self or for service. It is a place in which a person can dwell, a place that is so easily affected by corruption, as people worship the art form instead of the great artist himself!