There are some well-worn cases of people taking a few rounds of .25ACP and continuing to fight, but could we not cite cases involving .45ACP and .357 Magnum?
Regardless of caliber and even shot placement, a person who takes a bullet is going to be discouraged from continuing to fight and at least partially disabled from the same. Just how discouraged and disabled will vary a lot, but taking a round will always result in some degradation in fighting ability. That is why so many people advocate, for those who must carry something tiny or carry no gun at all, carrying a small caliber mouse gun.
I have started working toward carrying a pocket .380, specifically a TCP. The thing is really small, very light, and so far reliable with decent ammo (it does not like steel cased stuff). I have not tried any JHPs yet and may never, since I plan to carry ball ammo.
Most of my workplaces preclude carry, so I like to keep something in the car in a lockbox. When I dress for going someplace where I can carry, I test carry the TCP for a while before I head out the door, and I find that it virtually disappears on my person whether I'm wearing shorts or a suit. Since I don't expect to need more than 13 rounds on most days (that was a joke--get it?), one in the pipe and two mags full will do until the mongol hoard comes charging over the hill.
As for the .380 round being powerful enough to save my life? You bet it is--if I mostly hit my targets.