At best, Caesar would probably have known about as much as we do; at worst, his understanding would have been heavily fictionalized. Our most important source for Alexander's life and deeds is Arrian's Anabasis of Alexander from the 2nd century AD, which is according to the author an attempt to "get the story straight". It is mainly based on the account of Alexander's companion Ptolemy Soter; Arrian presents the reasoning that Ptolemy generally seemed to tell the most plausible story, along with the more dubious argument that Ptolemy, as a king, would have been particularly dishonored by telling a lie. He also employs to a lesser extent the writings of other contemporaries like Aristobolus and Nearchus.
Earlier writings on Alexander, like that of Diodorus Sicilus (a contemporary of Caesar) and Plutarch, chiefly employed a now lost work by a writer known as Cleitarchus, who, by both the contents of these works and ancient commentary, appears to have been more concerned with writing a read-worthy epic than getting the facts straight (even on matters like geography), and it is clear that his account was very influential.
To my knowledge, there is no attestation of what, if any, works on Alexander Caesar read. If Caesar or someone else in Caesar's days had been as discriminating and critical as Arrian, we can probably reasonably infer that they would've had access to at least some material that was lost to Arrian two-odd centuries later, and thus knowledge lost to us (whether they would have been able to effectively sort such material out from less reliable records is another matter). Barring that, if Caesar had read Ptolemy and Aristobolus, it is likely he would have known about as much as we do; perhaps more able to contextualize some aspects than us, less able to contextualize others (again, how he would have contextualized his reading, e.g., exaggerated army sizes, is harder or impossible to say).
Alternatively, had he read and mainly relied on the work of Cleitarchus, which seems to have been very popular, then he would have come away with a much more fantastical picture. We could speculate back and forth about whether Caesar like Arrian would have preferred the work of a military man or not, but that doesn't seem like a very fruitful exercise.
Alexander falls into the unfortunate category of characters who were semi-mythical probably within their own lifetime, and who therefore quickly become veiled off to inquiry and understanding; this is really a factor that matters much more than the space of time between events and writings. Judging the sources we have is a tricky task, given how poorly we understand the Achaemenid Empire at the time, and I am personally inclined to doubt the accuracy of Alexander's military accomplishments and the odds he faced as they are presented. The stage seems to have been set for a political crisis and internal power struggles crippling Dareios right around the time of Alexander's invasion, yet these seem oddly absent until after Alexander's victory at Gaugamela, with accounts of Alexander tactically manipulating and personally humiliating Dareios (who was an accomplished military man while Alexander was still an infant!) dominating the accounts of their clashes.
Needless to say, Caesar is unlikely to have been in a much better position to critique these aspects of histories of Alexander than we are today. I tend to believe that the events of Alexander's conquests should be regarded as much murkier than they are commonly reported, but given his position in the western canon, the bordering-on-repulsive exaltation of him as a virtuous hero, and the diminutive interest in the Achaemenid Empire, this is unlikely to happen any time soon.
Probably we know LESS about the actual person that was Alexander the Great than Julius Caesar might have.
About the 'enigma' Alexander we know a lot, because a lot of people have written about him, but since most of them wrote well after Alexander's death or refer to sources by contemporaries.
Our sources consist basically of the sources of sources.
Diodorus especially probably referred a lot to Kleitarchos, a historical writer who was alive during the time of Alexander the Great and wrote a depiction of the Alexander Campaign (though it is unknown if Kleitarchos himself ever met Alexander). All of Kleitarchos' works are lost to us, except for fragments from different authors who mention him (like the aforementioned Diodorus). However, his work was apparently very fictionalized and overexaggerated so it's questionable how much of his work could have been trusted to paint a realistic picture.
Then there were also a lot of letters and ship diaries, which were the basis for authors like Nearch, Aristobulos and Ptolemaios, all lost to us, but all three a huge basis on Arrian, a writer living around 200 AD, in his Anabasis (a name taken from Xenophon, who, in turn, was a huge influence on Caesar).
Their depictions of the expedition were more critical, especially Ptolemaios made the aspiration to tell only the truth. And Aristobulos because he fought at the side of Alexander.
From Arrian's Anabasis 1 (Translation by E. J. Chinnock, which I quickly got from the web, because I mostly deal with German translations)
"But in my opinion the narratives of Ptolemy and Aristobulus are more worthy of credit than the rest; Aristobulus, because he served under king Alexander in his expedition, and Ptolemy, not only because he accompanied Alexander [...], but also because he was himself a king afterwards, and falsification of facts would have been more disgraceful to him than to any other man."
Of course, that latter part is basically bollocks, at least that's not how we can infer that Ptoleimaos was telling any sort of truth.
However, to come back to your initial question, since a lot of works from the 100 - 200 AD time survives and they all used authors from 323 - 280 BC as their sources we can be reasonably sure that Caesar (who, as a Roman aristocrat probably also knew how to read Greek) also read those accounts and therefore knows more about the person of Alexander than we do, because there was less time to greatly distort his image yet (which didn't mean it WASN'T distorted by the time of his death already, but less so).
The question still remains if Caesar knew the "real" Alexander any better through those sources, but he probably had to wade through a lot less sources than we did.