Nate - no, not necessarily. If the BG is high on drugs, or drunk, or is in a primitive state of absolute belief that bullets won't hurt him (don't laugh, I've seen this up close and personal!), then NO handgun round is likely to stop him absent a CNS hit (or two, or three...).
As for this thread: yes, the .38 Special is a minimally acceptable defensive round. I say "minimally" about it (as I do about 9mm. Parabellum) because there are plenty of horror stories of failure-to-stop in these calibers. Sure, there are such stories about every caliber, but there are more of them about these two... In my .38's, I carry the FBI load of a lead semi-wadcutter hollow-point at +P velocities. It's got the best street record of all, equal to a .45 ACP FMJ, and if I put 'em where they need to go, I'm reasonably confident of the outcome.
However, NEVER expect one round to get the job done. As Clint Smith so eloquently puts it: "Shoot what's available, as long as it's available, until something else becomes available!"