There's no reason to think so. His more famous remarks are a good guide to this. When explaining why he was divorcing his wife amidst the Good Goddess scandal, for instance, he said "my wife ought not even to be under suspicion" - not the oft-seen "the wife of Caesar must be above suspicion." In the next chapter, he refers to himself in the first person when talking about how he'd lived as long as Alexander but had no great success to show for it. Asinius Pollio recorded him as talking in the first person after the battle of Pharsalus about how he would have been prosecuted and disgraced if he had not invaded Italy. And he wrote "veni, vidi, vici," not "Caesar came, Caesar saw, Caesar conquered." You get the point. There are countless examples of him referring to himself in the first person. And even to the extent these famous quotations aren't his actual words, consistently referring to himself in the third person would have been an unusual affectation that the sources would certainly comment on. He famously wrote in the third person in his account of the conquest of Gaul, and may well have referred to himself in the third person from time to time, but not consistently.