Will using egg whites instead of whole eggs have an effect on the finish product when baking?
It will definitely make a difference. Yolks contain various things like fats and emulsifiers that affect the flavor and texture of baked goods.
If you want more details, then tell us what you're baking.
According to ChickenPing (http://www.chickenping.com), you can use 2 yolks and 1 tbsp water (for cookies) OR just 2 yolks (for custards).