Is crowdfunding a possible way for economic development agencies to help their local businesses?

Possibly.

However, if that were to be done one business at a time it would likely result in the same difficulties that individual small businesses (especially startups) would have. Liquidity (or lack thereof) in such an investment creates resistivity on the part of the investor public. 

Instead of helping to use crowdfunding on a one-on-one basis, I believe a better approach is to have those agencies form a pooled fund that can be taken public and have that pooled fund do the investments in those individual companies. That way the companies get the money they need but the investors can have the liquidity of a public company.

See this article I wrote on the topic: How to Increase the Flow of Capital to Small Businesses While Enhancing Liquidity for Investors (SBHCs) 9/6/2016 https://www.linkedin.com/pulse/how-increase-flow-capital-small-businesses-while-michael-sauvante//