Of course. As someone who ticks most boxes on the privilege checklist I can witness first hand how much easier that has made my life compared to several of my friends and colleagues who ticked far fewer boxes. At the same time I've known people from even more privileged backgrounds than me completely fuck their lives.
So while coming from a 'privileged' background is important, and perhaps even necessary, in becoming the next Elon Musk, it is far from the determining factor.