Train classifier on balanced dataset and apply on imbalanced dataset?
Is this a problem?


No. not at all.


  Will the model reproduce the trained target distribution from DS1 when
  applied on DS2?


No, not necessarily. If 


Balanced set DS1 is a good representative of imbalanced (target) set DS2, and
Classes are well-separated (pointed out by @BenReiniger), which holds easier in higher dimensions,


then model will generate labels with a ratio close to imbalanced DS2 not balanced DS1. Here is a visual example (drawn by myself):



As you see, in the good training set, predictions resemble the real-world ratio, even though model is trained on a balanced set, of course, if classifier does a good job of finding the decision boundaries.