François Derrien, Ambrus Kecskes, and Phuong-Anh Nguyen have a new paper on this topic, and basically the answer is yes, because of labor supply effects:
We argue that a younger labor force produces more innovation. Using the native born labor force projected based on local historical births, we find that a younger age structure causes a significant increase in innovation. We use three levels of analysis in succession – commuting zones, firms, and inventors – to examine or eliminate various effects such as firm and inventor life cycles. We also find that innovation activities reflect the innovative characteristics of younger labor forces. Our results indicate that demographics increase innovation through the labor supply channel rather than through a financing supply or consumer demand channel.
Here is the SSRN link.