Baking – Cake without baking soda

I have this delicious recipe for flourless almond cake:

• 1 1/2 cups whole almonds, toasted
• 4 large eggs, at room temperature, separated
• 1/2 cup honey
• 1 teaspoon vanilla extract
• 1/2 teaspoon baking soda

• 1/2 teaspoon salt

  1. Process whole almonds in a food processor or blender until finely ground (you will have about 13/4 cups ground). Beat 4 egg yolks, 1/2
     cup honey, vanilla, baking soda and salt in a large mixing bowl with
     an electric mixer (or use a paddle attachment on a stand mixer) on
     medium speed until well combined. Add the ground almonds and beat on
     low until combined.
  2. Beat 4 egg whites in another large bowl with the electric mixer (use clean beaters on a hand-held mixer or the whisk attachment on a
     stand mixer) on medium speed until very foamy, white and doubled in
     volume, but not stiff enough to hold peaks, 1 to 2 minutes (depending
     on the type of mixer). Using a rubber spatula, gently fold the egg
     whites into the nut mixture until just combined. Scrape the batter
     into the prepared pan.
  3. Bake the cake until golden brown and a skewer inserted into the center comes out clean, about 28 minutes.

I know a friend who is allergic to baking soda and baking powder. What will happen if this recipe is made without baking soda? Will it collapse although I had beaten the egg whites? Aren't they responsible for making the cake rise?