Yes broken toes can heal on their own even without medical treatment.
A broken toe is rarely serious enough to need to go to the emergency room and usually at home care can help the broken toe heal.
A broken toe usually takes between 4 weeks to 6 weeks to fully heal but if the broken toe does not heal within 6 weeks or you have more pain, swelling etc then see a doctor or go to the emergency room.
I've broken my toe before and just allowed it to rest and heal on it's own and within 6 weeks the broken toe was fully healed.
I just tried my best to stay off the broken toe but if you want to or can walk some it's okay to do so.
But if you have any pain with the broken toe then it's best to avoid putting weight on the toe that is broke.