According to the mythological "rise of the West" narrative so firmly ingrained into most Westerners, yes. According to recent academic research, not really no. Life is much more complicated than a simple inheritance from one source.

For some works that are critical of the traditional Western "rise" story that is based of Roman/Greek foundations, check out:

I love Jack Goody's The East in the West. Related to this question and super good read. His Theft of History is also super interesting.

Martin Bernal's Black Athena would be interesting reading related to this. Although elements of it are really problematic, it has some interesting thoughts. See his later publication, Black Athena Writes Back: Martin Bernal Responds to Critics - to look at some of the controversy/issues relating to this book (poor use of archaeology, weak suppositions, spurious etymology,etc).

This is a very old, Victorian mind set. Read Millennium by Tom Holland. The Roman Empire had a lot to do with foundation of cities and the building of roads and infrastructure in Western Europe but Oppida were already springing up around Europe before Roman conquest. The idea that the romans tamed savagery in Europe is simply not true.

Add to this the fact that when the Roman Empire collapsed, it truly collapsed. Buildings were left to crumble, stone left to be pilfered, Europe left to rot essentially while they all pissed off to Turkey.

Charlemagne, his Christian conquests and the decision by his son to divide his kingdom into three separate kingdoms was far more influential on the politics of modern Europe, particularly when you consider this is when the border between what would be France and what would be Germany was laid down.