Is there any particular reason you want to mix the two or is this just curiosity?
When a baking formula is developed it is a mini science project and provided the results are what you want I for one tend not to mess with it. Mostly because I am not good enough to second guess the expert.
i'vew been baking gluten-free for a couple of years now and have used cornstarch as one part of my flour mix - i've never had a problem with using it and yeast. gluten free baking is much different than traditional gluten based recipes. pm me if you want a good sour dough recipe.