Forward voltage across the diode
Your question can be paraphrased as ...


  If we take a model of a diode that contains a certain parameter, and set that parameter to zero, then please confirm whether or not this consequence will occur.


It's sort of implied in your question that you find this predicted behaviour incompatible with what you'd expect from a real diode. It is. 

If you set up a model, which you might expect to be valid (ie match reality within a certain error) for a certain range of parameters, and then set one parameter outside that range, then you can reasonably expect to get incorrect predictions from your model.

The 'barrier potential' + 'dynamic resistance' model of a diode is very simple, though better than the 'voltage drop = 0.7v' model which works just fine for 95% of applications. There are better models, if you're having trouble with the accuracy of these two.