So obviously Chagatai (also known as Old Uyghur, Old Uzbek, or Sart) was frequently used as a lingua franca, for literary purposes, in administration, and by some members of the upper class in Central Asia between 1400 and 1900, but was it ever spoken by a majority of the common people in any particular region?
To some extent, yes, it was in areas with an Uzbek/Sart majority. That said, the spoken language probably varied to a greater or lesser degree with the written form. The relationship between Chaghatay and Uzbek is pretty similar to Ottoman Turkish and contemporary Turkish. It would have also lived alongside earlier versions of Tajik Persian, Kyrgyz, Turkmen, Kazakh, etc.