My grandmother, in the age and firmly of the belief that a woman should be put to sleep as soon as there was any sign of labor gave birth to my father (her 3d) in the car on the way to the hospital. She never talked much about birth (except to say that she couldn't fathom why a woman would refuse pain control and that the idea of breastfeeding, well, not HER body!) but I'm pretty sure that if she had any impending signs she would have been there sooner.
My best friend had three precipitous births. The first, her blood pressure was high that morning (in retrospect, a sign of labor), so she was hospitalized, on monitors, etc., and nothing to indicate she was in labor until within 25 minutes of the first birth (twins). The second, she had been told to go on leave from 36 weeks to monitor for 2 hours a day to catch any "silent" contractions, and still, despite having seen nothing at all to indicate any contractions the night before, woke up at 7 with contractions and gave birth at 7:30 (in her bathroom). The third, same deal with taking leave, noticed some hardening of the uterus at noon (was supposed to "monitor" by spending 1/2 hour every few hours relaxing with her hand on her belly to feel for uterine hardening), ran to the hospital ASAP and gave birth within minutes of arrival.
Another friend, with #2 thought she had weeks left to go because that morning's check up had shown minimal effacement and no dilation and besides she had no signs of anything happening, water broke in the grocery store and she gave birth 20 minutes later in the hospital waiting room (hospital 5 minutes from store). With #3, felt sluggish one evening, baby born at home 1/2 hour later.
So yes, my almost-personal experience makes me believe that a woman can give birth with little to no "prep."
Now for me, with #1 had sporadic contractions from Sat., regular 15 minutes from Sunday night, 2-3 minutes from Monday night, gave birth Wednesday morning. So plenty of prep. With #2, regular contractions all night Wed. night and Thur. night, very few during the day. Friday sporadic contractions all day. Friday night active labor, birthed near midnight on Saturday. Plenty of prep all around. Hadn't been checked either time until arriving at the hospital deep into transition (with #1, around midnight Tuesday; with #2 at 10:30 PM Sat.), both times between 8 and 9, so no clue how long I was actually dilating.