I think that Rand's syntax, along with her diction, help to develop Equality 7-2521's character through the use of one word: "We." The reason I use both is that I think this falls more under "diction" than "syntax." However, I think syntax is important in the tone that the word "We" creates for the character.
Rand's choice to use "We" instead of "I" is primarily to create the effect of community in the society. There is no such word as "I," because it has been outlawed. Instead, the citizens all refer to themselves as "We" to remind themselves that they are never alone. Nothing they do is ever on their own. They are a part of something greater.
The use of "We" also lends a grandness and importance to everything that is done in the society. This is where I think you could argue that syntax comes into play. It's not necessarily a matter of word order but rather the mood that the words create when put together. When Equality 7-2521 and International 4-8818 discover the tunnel, their conversation is one of extreme seriousness. International says, "We shall report our find to the City Council and both of us will be rewarded." This comment is responded to by Rand and then Equality 7-2521 himself:
And then we spoke. Our voice was hard and there was no mercy in our voice. We said:
"We shall not report our find to the City Council. We shall not report it to any men."
You can see the seriousness this lends to the action itself.
Finally, the use of the word "We" throughout the story makes the use of the word "I" in the end that much more effective. Through this one simple change, Rand creates a monumental point for her story. Equality 7-2521 says:
And now I see the face of god, and I raise this god over the earth, this god whom men have sought since men came into being, this god who will grant them joy and peace and pride.
This god, this one word:
As you can see, the transition is powerful for both Equality 7-2521 and the audience.