Can studying the sword make you smarter? It is debatable, but according to a paper written in 2011, the development of stone tools and weapons by prehistoric humans 80,000 years ago contributed to the development of the human brain and how it creates complicated processes. So on a certain level, studying the sword could make one smarter as one creates different strategies or methods while studying its use as well as its history, manufacturing or accoutrements, but the biggest benefit to studying the sword is that it can improve one's Aikido skill.
In O Sensei's time, the students he accepted into his dojo already had acquired martial skills or were proficient in the use of the sword. For instance, Nobuyoshi Tamura Shihan's father was Kendo master and he grew up studying the sword. Therefore there was no need to teach them the "basics" of sword use. O Sensei's sword work was so enlightened that many of those students professed that it was over their heads.
The movements of Aikido are based upon the use of weapons namely the sword and the jo, but more specifically on the movements of the Yagyu Shinkage ryu school of swordsmanship. Studying the sword brings context to the Aikido movements that we do practice every day in class. Knowing "why" sometimes gives us the anchor that we need to learn faster and become more proficient. I know that for me, I wish that I had studied Iaido sooner and didn't wait until after Furuya Sensei had passed away.
Can studying the sword make us smarter? I do believe that it can in the way that learning new things keeps us young. Studies have shown that people who are lifelong learners and exercisers are less likely to suffer from Alzheimer's disease. As an added benefit, it will make our Aikido skill much stronger too.
Sources: http://www.kurzweilai.net/cutting-edge-training-developed-the-human-brain-80000-years-ago http://www.sciencedirect.com/science/article/pii/S0047248411000595