I'm looking for a good academic source that answers the depth of this question. I've read a lot about ancient sites with astronomical alignments (such as Nabta playa) and how astronomy was important for establishing calendars (such as the Egyptian calendar based on the heliacal rising of Sirius in ancient Egypt) but I can't seem to find a source specifically regarding the importance of astronomy in shaping early civilization. It seems evident that it did have a huge influence on early civilization ie the astrotheology/astrolatry of the ancients and the fact that it was important for timekeeping, establishing calendars, celestial navigation, etc... If you know of any good material on this subject matter, I'd appreciate it. :)
I would most heartily suggest Early Man and the Cosmos by Evan Hadingham (1984). It's a little dated but if you're looking for a good survey of several astronomical traditions across the prehistoric world, there are few alternatives. Being a New World fella, I also would suggest Anthony Aveni's compiled reader New World archaeoastronomy, aptly titled Foundations of New World Cultural Astronomy (2008). That one's got a lot of good discussions and dialogues about North, Meso, and South American cultural astronomy.
Hope this sets you off on the right path! Archaeoastronomy is a burgeoning field, but it's also currently got some whackadoos floating around (see: The-Show-That-Must-Not-Be-Named). Getting into the field from these reputable academic sources will help you figure out the folks who know what they're doing.
EDIT: I suppose that I could give you my own input on your title's question rather than just pointing you to sources, as well :)
The answer to your question, I would argue, is an emphatic "yes". Humans are pattern-builders and interpreters. We see cycles and behaviors throughout nature. People across time and space have observed these patterns, and found power in the ability to communicate and anticipate them. A good grasp of the solar year allows for anticipating the coming of rains, and the necessary timing for prosperous, efficient agriculture. A major factor in maintaining an administration's effectiveness - and their legitimacy - depends on everyone being on the same page temporally and spatially. The sky is omnipresent and accessible to all people; it has been an excellent tool for growing, controlling, and maintaining polities spanning entire continents.