Sponge cake with only three ingredients - will this work at all?
The key to this cake is the whisking of the eggs and sugar to the ribbon stage.  This incorporates a significant amount of air into the batter.  You didn't mention it, but I imagine the flour is then folded in.

The cake will work mechanically.

However, I cannot imagine it will taste very good:  there is no salt to enhance flavor, no fat (other than from the eggs), and no flavoring such as vanilla.  So the only significant flavor will be from the eggs themselves.  

As to how long it will keep, I imagine it would freeze well; it will probably keep at room temperature for 2-3 days.

Update: I see from the link added to the question that these layers are intended to be used in layer cake with other flavors and components, where its neutrality is actually a virtue.  I still think it needs about 1/2 tsp of salt, and maybe a touch of vanilla or even pistachio extract if you can get it, but the neutral flavor makes sense in context.