Yes you should see a doctor when you have a broken toe.
Most broken toes are nothing serious and usually resolve and heal on their own even without medical treatment.
However if you don't go to the doctor to have the broken toe fixed then the broken toe could possibly get infected which is not a good thing.
I've had a broken toe before and went to the doctor just to be safe and they put a cast on the broken toe to help it heal and said that if it seemed to become infected or get worse to come in again.
Luckily the broken toe healed within 6 weeks and didn't get infected but there's the possibility of the toe becoming infected.
Most broken toes however heal pretty good even without medical treatment but if you do have a broken toe it's best to go the doctor or urgent care center to have the broken toe fixed.
If you leave the broken toe untreated then there's a possibility of infection.
So to be safe see a doctor or go to urgent care or emergency room just to be safe and prevent further issues and possible infections from the broken toe.
Most broken toes usually heal within 4 weeks to 6 weeks but if it doesn't heal within 6 weeks then you should see a doctor about it.
If you think the broken toe is becoming infected or the toe is swelling, increases in pain etc then see a doctor about it.