"Had Custer won, Garryowen would be considered nothing but a flagrant symbol of white conquest of Native Americans."

I doubt that. I imagine it would be remembered merely as another old handed-down tune, the way it is now, for the most part. (Example: I learned the tune as a child; at some point in my adult life, I learned of the Custer connection. I'm certain that my mother, who had taught me the tune, knew nothing about the Custer connection.)

In fact, if Custer had won, I doubt he himself would be widely remembered. It was his dramatic end that immortalized him.