Yes, they can. At least, if they are tamed. I have pulled natives out of booths twice, and saw they are at the beginning of pregnancy.
My main source of food is animals that get caught in traps. I have just 2 traps - one wooden cage, and one bear trap.
When they are in your inventory, hover over them and press T to dismantle.
You can also hunt animals yourself. Pigs and chickens are the easiest prey, but deer are also doable.
In the early game, berries are the perfect food, because they also provide water. Later on, you'll have raincatchers and wells, but early on, water would be harder to get than food.
Later in the game, you'll be setting up food production with natives to care for crops and animals.