no you won't.
idea of a birthing rack is three issues...
#1. allows mother to rest by removing her from immediate exposure to male after giving birth which would most likely result in her getting pregnant within days of giving birth
#2. removes male from exposure to offspring that will hopefully result in fewer deaths
#3. allows mother and offspring access to food.
problem I see with this logic is that mothers will fight over babies and food, so unless you plan to keep each litter and mother in their own bins...mothers will still tend to restrict each other and the babies optimum access to food and losses from fighting will still occur
without birthing racks you will get slightly less output but you will use less resources.