I can see the potential in that but thats not how most civilizations end. Perhaps half did meet there end in that fashion, but many more met their demise in either two ways or both:
1. Foreign Conquest
2. Internal Decay.
And not to say that you're entirely wrong, but the historical use of the term "Dark Age" and the cessation of civilization are two different things.
The outcome you're envisioning is certainly dark, it has the potential to end civilizations, and it can last to where it can be called an age (i.e. Bronze Age, Iron Age, Industrial Age), but to call the catastropic,ecological dearth "Dark Age" would redefine the term.