It has nothing hideous in it, and only the view
is beautiful; it shares nothing with the city except the overarching sky.

In order to determine if there is symbolism in "the overarching sky," we must first clearly understand what the sentence (added above) is referring to. In context, the sentence refers to the British government civil station. It is a nondescript building of no particular character but of no particular offensiveness either. It is a serviceable building, "sensibly planned":   

As for the civil station itself, it provokes no emotion. It charms not; neither does it repel. It is sensibly planned, with a redbrick club on its brow, and farther back a grocer's and a cemetery .... It has nothing hideous in it, and only the view is beautiful; it shares nothing with the city except the overarching sky.

There is  nothing charming about the station, and there is nothing "hideous" or terrible about it either. The only quality of beauty about it is the outward view that can be had from its environs. Most importantly, the civil station shares nothing with the Indian city of Chandrapore except what neither can escape, the sky that covers both: the overarching sky. Let's identify the symbolism in this and we may find if there is symbolism in "overarching sky."

The civil station symbolizes the British in Chandrapore. The outward "view" symbolizes India. The British, like their building, have neither charm nor hideousness. They are sensible, like their building, yet, also like their building, they have a "redbrick club" on their metaphoric brows symbolic of the psychological brutality of colonial oppression and dehumanization of Indians, as is brought forth in the conversation in the next chapter. The British are also symbolically related to death (physical and spiritual) by the presence of the adjoining cemetery, “farther back a grocer's and a cemetery....”

Now to analyze possible symbolism in "overarching sky." This represents a literal physical reality. This literal reality is that the sky covers both British and Indian, no matter what they feel about each other, no matter how different they are from each other. And, yes, the presence of a sky that covers both British and Indian symbolically represents the vast differences, the vast philosophical and cultural and social gulfs that separate British and Indian: they are so separate from and so isolated from each other that the only thing, the one and only thing they share in common is the sky overhead, the overarching sky.

The significant symbolism presented in the description of the civil station and, more importantly, in “the overarching sky” sets the psychological backdrop that is critical to the next chapter, Chapter II, in which the Indian friends, Aziz, Mahmoud Ali, and Hamidullah, discuss the possibility of friendship  with the British.

[T]hey were discussing as to whether or no it is possible to be friends with an Englishman. Mahmoud Ali argued that it was not, Hamidullah disagreed, but with so many reservations that there was no friction between them.