Almost certainly not. For one, he was illiterate, as was the vast majority of the steppe tribes. Mongolian was an unwritten language until Genghis Khan ordered a script be developed for it, which was based off a dying derivitive of Aramaic. Two, even in China, which was a strong scholarly state, they vaguely knew of Rome as they had indirect trade through the Silk Road and contact with Turkic and Iranian civilizations. Three, if they knew any specific individuals, it would have almost definitely been Augustus Caesar, not Julius Caesar. Remember, Augustus was the first emperor of Rome, not Julius, and was the one to propagandize the idea of a divine eternally powerful empire (like China had done already).

As far as who he looked up to, its impossible to know, but its 99.9% chance its nobody we have ever heard of. You have to realize that there is just about nobody in history to have such a large impact and remain such a mystery, besides maybe Jesus Christ and Alexander the Great. We have essentially 0 contemporary sources about him. We dont really know where or when he was born, how or when he died, or the majority of his life details besides what was passed down through oral tradition and then written in the "Secret History of the Mongols." If you read it, you'll notice that much of it sounds very mythological.

I cant answer your followup in any academic way. As an aside, Ill say that "who he looked up to" would not have been a historical figure, but either somebody he knew personally, or a traditional legend. Perhaps his mother. Perhaps whomever trained him in archery and horseback riding. Perhaps a Mongolian mythical hero. Thats as far as I can tell you.

A follow up a question: was Genghis Khan literate? How much education did he receive?

If the answer is "no" for Julius Caesar, what about Alexander the Great?

I would strongly recommend "Genghis Khan" by Frank McLynn. I've just started and it provides very detailed analysis of the sources that are available to us today, as well as explanations of modern hypotheses about Genghis Khan.