Interesting question, considering how this event changed from the initial script.
It is very clear that Elle did indeed die in the original script - but the film does not show her death, although it is implied by the sighting of the black mamba.
Her death appears in this segment from the original screenplay:
Elle drops the Bride's sword.
As her blood continues to escape, both women look across each other.
The effect is that Elle Driver is a balloon and her life is escaping
before both their very eyes. And now looking across at each other, the
two women see the other for the first time, not as adversaries, or
opponents, or as rivals, or as bitches...but as sisters.
Elle no longer has enough life in her to stand up...She falls to her
knees in front of The Bride....
...then as she dies, she leans the side of her head against The
Bride's standing body. Her blood runs down The Bride's leg. As she
passes on, Elle gently wraps her arms around the Bride's leg.
The Bride's hands go down to Elle's long blonde hair, and begins
gently stroking it, easing her pain as she expires.
Only in death do they find the sisterhood that could have been theirs.
As you can see, this is markedly different from the final film. In this version of the script, Elle has already killed the black mamba, so she dies from her wounds after fighting Beatrix. In the film, she is left blinded by the bride, with the sound of the mamba growing ever closer.
It appears Tarantino always intended for Elle to die, but left her death offscreen in his final version.
You can read the full script at the Internet Movie Screenplay Database.