Not only does investing in the arts stimulate economic growth, it also stimulates our culture. There are more up coming artists around and we invest in their "product." We like the "product" and we tell others and they buy the art. The more bought, the more the artist makes and the more the artist can make more art. Economic growth!
Any time the government invests money in any sector of the economy, there will be gains. The arts is no different. The more people are employed gainfully and making money, the more they will spend in the stores around them. That means businesses make money and can possibly hire more employees. This country doesn't appreciate art all that much, which makes things like the NEH and NEA easy targets for conservatives.
Investing in anything will help stimulate the economy. It is just a matter of to what degree. For example, investing money in a play will support businesses such as hardware stores, advertising companies, hardware stores, printing companies, and more. It will also provide wages directly to the actors, stage hands, and theater employees.
Investment in anything will stimulate the economy. The arts is no different. In vesting in the arts could be in a wide range of things. Most of which could help the economy. As long as you are spending money you are stimulating the economy. So of course this will help and is a good thing.
While the arts are an important part of culture, investing in them is not a good catalyst for economic growth. We should invest in the arts, but not as a stimulus. We need to invest dollars for economic growth in the fields that will benefit the most people, the industries and services that (unlike the arts), can provide hundreds of thousands of jobs.