Yes you can use yogurt in place of eggs in cake mix.
The purpose of the eggs in cake mix and cakes is to bind the eggs together and also add moisture to the cake.
When you don't use eggs in cake mix or any egg substitute such as yogurt in cake mix the cake mix won't bind together and may fall apart.
When eggs are added to cake mix the eggs proteins coagulate in the cake, helping to create the overall structure of the cake.
If you don't use enough eggs in the cake mix the cake may be to soft and flat and if you use too many eggs in the cake mix the cake may be tough and chewy.
When you use yogurt instead of eggs in the cake mix you use 1/4 cup of yogurt to 1 egg.