Atsushi Yamada conducts New york City Opera this week in Tokyo. “Mr. Yamada’s rise to the podium is a testament to the spirit of artistic entrepreneurship: he helped raise millions of dollars for City Opera’s foray to his native land, its first overseas tour in almost 20 years. But it also leads to questions about the role big money plays in the arts, particularly in the cash-desperate world of classical music, and how it influences artistic choices. Mr. Yamada, 41, studied and worked his way onto the City Opera’s conducting roster; the company says he is a genuine talent and is well liked at the house, where he is an established presence, having conducted eight performances so far. But he also had the backing of a City Opera board member who was his boss at Sony, a longtime supporter of the opera.