This particular recipe is based on a French custard (anglaise). The fat and emulsifiers/proteins in the egg yolks hold moisture and interfere with the formulation of ice crystals, which gives the ice cream an incredible silky texture once frozen. I would be hesitant to substitute whole eggs. You can definitely try it, but you cannot expect to get the same creamy result.
Pastry kitchens never ever throw out egg whites. If they can't go through them, they freeze them for use in other products. Here's a good site that lists
many ways to use leftover egg whites.
If you don't want to use egg yolks, you can make a
Philadelphia-style ice cream. These types of ice cream do not contain any eggs. Cheers!