Yeasted bread rises because yeast gives off carbon dioxide as it metabolizes sugars in the dough. This carbon dioxide fills the pockets between the sheets of gluten, causing the bread to inflate like a honeycomb of little balloons. This happens before the gluten has a chance to form. When one kneads the dough to develop the gluten, one flattens any gas pockets which might have formed. Also, chemical leavenings have a destructive effect on gluten, so one would be working at cross-purposes to begin with.
Unyeasted breads are like yeasted ones in that they rise via a multitude of little gas pockets.
The difference is that in unyeasted breads, these pockets are more like little bubbles floating in a thick emulsion, not rubbery balloons between sheets of elastic gluten. When baked, the solid which holds them in place is not coagulated gluten proteins, but instead a more tender collaboration of gelatinized starch and coagulated egg proteins. To summarize, the challenges in making breads, cakes, muffins, and suchlike is first to get tiny bubbles into the batter or dough, and then to keep them there during mixing and baking, so that other ingredients can solidify around them. So the trick in making light baked goods is to make a batter full of tiny air bubbles, and then provide a structure which will solidify around these bubbles, so your cake doesn't fall. There are several traditional ways to incorporate air in your baked goods, and some of which are easily used in vegan baking, and others which may be adapted to vegan ingredients.