No. Each dot in the graph below represents a nation: Change in education on the x-axis and change in per capita GDP growth on the y-axis.  Between the 60’s and the 90’s every country in this sample boosted its average years of education–it was a golden age of alleged human capital investment.  Some nations boosted schooling more, some less.  How did that turn out? 

On average, no relationship.  The trendline points down slightly, but for the time being let’s just call it a draw.  It’s a well-known fact that countries that started the 1960’s with high education levels grew faster (example), but this graph is about something different.  This graph shows that countries that increased their education levels did not grow faster.  
And it’s not just me saying this: Here’s James Hamilton and Josefina Monteagudo, who ran a more sophisticated version of the same test:
Another troubling aspect of our results is that investment in human capital [measured via secondary education] seems to have nothing to do with changes in growth rates over time.
Lant Pritchett’s paper on the topic is summed up by the title: “Where has all the education gone?”
Some might look at these results and say, “Higher education actually is great for entire countries, but these studies just couldn’t discern that greatness. After all, correlation isn’t causation.” 
But that claim creates its own puzzle: If raising education really is so fantastic for countries, why can’t we find nation-level evidence of that?  We can easily find evidence that switching to faster money growth usually predicts higher inflation, that switching to more market-oriented institutions predicts faster economic growth.  The correlations show up just fine there–so why is data-torturing required when countries switch to pro-education policies?  
And if defenders of increased education want to claim that “We just need to do it right next time” then defenders of sound social science need to retort: “Then I’m sure you’ll understand if we absolutely insist on solid, experimentally sound evidence, along with proof of scalability, before we sign off on a nationwide program that will cost a couple of percent of GDP.”  
In a world of opportunity cost, “Let’s give it a try: It can’t hurt” should be a punchline.  
At our current state of knowledge, there seems to be little nation-level evidence that raising education levels in a country raises that country’s economic growth rate. 
What’s worth focusing in the meantime?  What kinds of economic changes within a country predict faster future growth in GDP per person?  Hamilton and Monteagudo again:
[I]nvestment in physical capital [and lower] population growth…seem to matter a great deal. 
Those of us who don’t like those results can take comfort: After all, correlation isn’t causation.