No. Even without the vast financial resources that are required for maintaining the elaborate framework that asserts art's status as the highest form of cultural expression, I believe that new art would continue to be produced. That said, art probably wouldn't be as much a part of culture as it is now without money.
Historically, art making has always been influenced by some combination of intrinsic and extrinsic motivations. At one extreme, a creative being's reward for making work is the satisfaction of the creative act itself. And at the other, art is produced purely for material gain. Sometimes, an artist does his best work when, subject to various constraints, he must rely on his own ingenuity and passion to accomplish his endeavor. However, it is also true that many of art history's most ambitious and important works could not have come to fruition without substantial and timely patronage.
The right mix of talent, intrinsic motivation, and external support is needed for a sustainable and vibrant environment for artistic innovation. The best example of this that I can think of is the now defunct NEA Visual Artists' Fellowship Program, which, for three decades, so considerately used its limited resources to have the greatest impact on American artists. All controversy aside, by deliberately choosing to fund the most promising artists precisely when they found themselves on the brink of a breakthrough, the NEA effectively managed to underwrite a very fertile period of artistic production in our nation's history. Art would not sink without money—but it can certainly become part of more peoples' lives with financial support.
—Joshua Chuang, graduate student, Yale School of Management