The economic systems of mid-14th century England, Eurasia, and northern Africa were just a mite different from the late stage capitalist system to which many nations currently ascribe today. There may be more flourishing, depending upon the metric one uses to measure actual prosperity, but the system is built on top of a rather precarious foundation that requires continuously expanding resources. As a minor example, look what one stuck ship sitting in a canal managed to do over a matter of days. Honestly, this whole system crashes every roughly 8 to 12 years and has to be fortified with an influx of new capital and resources, a modification of the books, and in 8 to 12 years it does it again because it's entirely built on short term gain.
So no, our system wouldn't survive WWIII and come out flourishing, it would have to evolve into a more robust, secure system. What that is I will leave to the reader, but suffice to say this one isn't it.