My partner and dear techie husband of mine were talking about whether
this techinique can actually inflict any sort of effect.  Although
surely unable to kill someone with this grip, would it be possible to
stun someone?  This is probably a yes/no answer, but I would love to
know!

Greetings, amberene! Thanks for asking for me. I'm always glad to
expound upon matters related to Star Trek.

If you'll recall, the "Vulcan death grip" was fictitious. It was a
ruse in "The Enterprise Incident" whose purpose was to convince the
Romulan commander that Mr. Spock had killed Captain Kirk. This
resembled the "Corbomite Maneuver," another scary-sounding but
nonexistent threat.

"Spock seemingly defects to the female commander on the scene in
return for retaining command as her mate -- having killed his captain
with the 'Vulcan death grip.' But all is a hoax: the captain returns
from the 'dead' to reveal their covert mission to steal a cloaking
device for Starfleet to dissect."

SciFi.com
http://www.scifi.com/startrek/episodes/59.html

The Vulcan technique which could cause unconsciousness is generally
called the "Vulcan nerve pinch" or "Vulcan neck pinch."

"Many Vulcans are skilled in a self-defense move known as the Vulcan
nerve pinch or neck pinch, which targets a precise location overlying
the baroreceptors of the carotid sinus at the base of the humanoid
neck, instantly rendering the victim unconscious. While practiced
mainly by Vulcans, it is not exclusive to their race; for example,
Data and Jean-Luc Picard have also mastered the technique, the latter
probably acquiring it during his mind-meld with Sarek."

WordIQ: Vulcan (Star Trek)
http://www.wordiq.com/definition/Vulcan_(Star_Trek)

Something similar to the "Vulcan neck pinch" is possible in real life:

"Carotid sinus reflex is basis of ?Vulcan neck pinch.? If you
stimulate carotid body in absence of actual increase in BP (by a
Vulcan gripping your neck and squeezing the carotid body) , resulting
decrease in BP from slowed heart will mean less blood to brain and
hence syncope (you will faint) Note this is distinct from certain Judo
neck holds which press on common carotid directly decreasing blood
flow (temporarily) to brain."

Brown University: Brainstem Principles
http://neuroscience.brown.edu/Coursehomepages/bn166/Brainstem.html

"A sleeper hold is a technique in which you apply pressure to the
carotid arteries, which are located on the sides of the neck, to
interrupt the flow of blood to the brain...
 
Many police departments forbid the use of chokes; martial artists
would be well-advised to do likewise. The sleeper hold is safer and
faster than the choke.  It can render a person unconscious in as
little as five to nine seconds, whereas a choke may take from one to
three minutes.  Although the sleeper hold is a safer method for
causing unconsciousness, care must be used when practicing these
moves, as well as when using them in an actual confrontation.  If the
pressure is held after the person loses consciousness, it could result
in brain damage - or worse."

LWC Books: Judo Chokes and Sleeper Holds
http://www.lwcbooks.com/articles/chokearticle.html

Google search strategy:

Google Web Search: vulcan "death grip" OR "nerve pinch"
://www.google.com/search?hl=en&ie=UTF-8&q=vulcan+%22death+grip%22+OR+%22nerve+pinch

Google Web Search: "sleeper hold" + "carotid"
://www.google.com/search?hl=en&ie=UTF-8&q=%22sleeper+hold%22+carotid

I hope this helps. Don't try this at home, kids. ;-)

Live long and prosper!

~Pink

dammit, he is right again :(

Nice answer, pinkfreud.

Out of curiosity, could an effective sleeper be applied as part of a
full-nelson?  Maybe by using a palm on each side of the neck?  It's
very difficult for one's opponent to fight back or escape from a full
nelson.

I was searching Google images for "full-nelson."  There are some
interesting results to say the least.
http://www.ahwgallery.com/May81/pic07.html

Daytrader,

I know a lot about "Star Trek," but I know very little about fighting
or defensive techniques. I pulled the term "sleeper hold" out of my
memory in order to use it as a search string, but I'm no martial arts
expert. I prefer the marital arts. ;-)

~Pink

May your marital arts never become martial arts.

I talked to AF tonight who said he had applied it successfully to many
people as a parlor trick, and he had it done to himself as well.  Of
course he has done a lot of other stupid things that no one else
should ever try.  But it does work.