What happens if a woman decides not to breastfeed her child? Will her baby still be well nourished?

Nourished, yes. Human milk is the optimum specialty item, designed so specifically that your own milk is better for your child than any other. There are transiently alive components, immune factors that reduce risk of infection that can not be replicated in the lab. We are blessed to have dozens of nutritious alternatives to help baby grow when BF in not chosen.You must do what you must do, but baby will do okay.
Usually. There are plenty of alternate substitutes for mothers milk available in products you can purchase at any drug store. It is generally recommended that all infants be breast fed for the first month as there is a transfer of antibodies which can be healthy for the infant and there is bonding with the child good for both mother and child. Your pediatrician can advise about nutrition.