Cake without baking soda
Honey is acidic with a pH of 3.9- that's more acidic than some oranges. There is also quite a lot of honey in this recipe that will give the acid the baking soda needs to react.

In this recipe, both the egg whites and the baking soda are going to provide some leavening.
Without the soda the cake will undoubtedly be a little more dense.

Additionally, even when not contributing to leavening, raising the pH will promote browning of baked goods. I think the ground almonds will give nice color but the recipe may be a little paler without the soda.

There is no soda in angel food cake and I expect this cake will also be just fine without it.