Are egg yolks neccessary for proper pancake structure in flourless pancakes?
Will it "work" in the sense that the batter on the skillet will coagulate and form a solid flat pancake-like thing?  Yes, it should.  That doesn't mean you'll necessarily like the results.

Keep in mind that the egg/banana pancakes aren't really producing something that tastes like or has the texture of a standard "pancake" (or even most gluten-free "flourless" pancakes).  The result will be something like a cross between banana-flavored custard and the middle of a piece of French toast.

However, yolks provide flavor and some tenderness (mostly due to the fat in them, which isn't present in the whites).  If you remove them, you might not like the flavor that results, so you might consider adding an alternative fat and/or something that can give more flavor (e.g., vanilla, complementary spices like cinnamon, nutmeg, etc.).  The "structure" shouldn't be worsened much without the yolks, but these "pancakes" don't tend to rise much anyway.  If you want something with a more airy texture somewhat closer to "normal" pancakes, you might want to add a small amount of baking powder and/or beat the egg whites and fold them in.

(Of course all of these additions and substitutions sort of defeat the purpose of the "super fast and easy" two-ingredient "pancake," but it really depends on whether you like the flavor and texture that results when you try to cook them, or whether you want to take a few extra steps to improve them.)