In recent decades, trade between nations has constituted an important component of global Gross Domestic Product (GDP), with official estimates showing that it likely accounted for a quarter of total global production. While evidence of association already exists in macro-economic data between trade volume and GDP growth, there is considerably less work on whether, at the level of individual granular sectors (such as vehicles or minerals), associations exist between the complexity of trading networks and global GDP. In this paper, we explore this question by using publicly available data from the Atlas of Economic Complexity project to rigorously construct global trade networks between nations across multiple sectors, and studying the correlation between network-theoretic measures computed on these networks (such as average clustering coefficient and density) and global GDP. We find that there is indeed significant association between trade networks' complexity and global GDP across almost every sector, and that network metrics also correlate with business cycle phenomena such as the Great Recession of 2007-2008. Our results show that trade volume alone cannot explain global GDP growth, and that network science may prove to be a valuable empirical avenue for studying complexity in macro-economic phenomena such as trade.