Yes, it can, but very very rarely.
Herpes is a very common infection, affecting about 60–70% of the world population under age 50 (source: WHO).
Most of the time, Herpes is just an annoyance, causing sores to appear on your mouth or genitals.
However, in rare cases, herpes can be life-threatening, if it leads to complications in your nervous system e.g. encephalitis or meningitis. This article explains further: Neurological Complications of Herpes Simplex Virus Type 2 Infection
These neurological complications are very nasty, and even if you are treated and you survive, your brain is likely to sustain permanent damage.
Some figures:
In USA, between 1999 and 2010, a total of 223 reproductive-aged women died of herpes-related conditions.
Source:
Mortality From Sexually Transmitted Diseases in Reproductive-Aged Women: United States, 1999–2010
STD Questions & Answers 