That is what all strangulation is. If you don't breathe your brain gets no oxygen from blood vessels.Do you mean if someone punches your carotid artery with a sharp blow it would kill you?
As TGY describes, there are different kinds of chokes, they are not all the same, they differ in terms of the mechanism (and speed) by which they cause unconsciousness & they also differ in terms of the potential to leave forensic traces.
A frontal compression of the neck impinges upon the windpipe. This restricts or nullifies the ability to breathe. Unconsciousness takes some time to occur, as the heart is still pumping blood to the brain & even without breathing this blood will still contain a depleting amount of oxygen. Unconsciousness will occur when the blood contains insufficient oxygen to maintain awareness. Death will follow if the airway remains closed.
This style of strangulation frequently leaves forensic evidence in the form of damage to small bones and cartilage of the neck. In a body with advanced decomposition such as in Karen's case, damage to the hyoid bone would still be visible if it occurred & it often does.
Another way to achieve a very similar asphyxia is by smothering, such as with a pillow. The mechanism & time until loss of consciousness is similar, but damage to the hyoid is far less likely. Given the time it takes for unconsciousness to occur, other physical injuries may be sustained during any struggling that occurs.
A very distinct kind of choke, referred to as 'guillotine' by TGY is performed by the application of pressure to the sides of the neck. This does not put pressure on the windpipe & thus there is often no damage to the hyoid. Breathing is still possible, but the blood flow to and/or from the brain is blocked by this technique. This means the brain is no longer getting blood circulation & unconsciousness can occur very quickly - within 20 seconds is quite common. Depending on the technique used, the amount of force required can be quite low & would at most leave soft tissue damage that would be undetectable in a corpse that has decomposed significantly. Given how fast unconsciousness occurs, there is much less time for struggle related injury - one would be starting to pass out seconds after coming to terms with their predicament.
Asphyxia by pillow, or a vascular choke would've left no remaining evidence on Karen's body.
edit it to add : just to be clear, a death vascular choke will leave forensic evidence (for example tiny blood vessels at the back of the eyes will often rupture), but these traces will be lost once significant decomposition occurs.