No, she is not a death eater, but many of her views fall within those of Voldemort's plans.
Magic is Might - Voldemort and the Death Eaters want to establish wizard power and authority over muggles. Also, they feel that any wizards or witches that are not pureblood, such as muggleborns and children of werewolves.
Umbridge agrees with this as we see in Order of the Phoenix where Sirius mentions,
"... she drafted a bit of anti-werewolf legislation two years ago that makes it almost impossible for him to get a job." (pg. 302)
Remember, Sirius says when asked this same question,
"I doubt it, I know her by reputation and I'm sure she's no Death Eater- ... but the world isn't split into good people and Death Eaters" (Order of the Phoenix, pg. 302)
Also, there are other interesting differences:
Dolores Umbridge hates all half-breeds, whereas, though Voldemort does not allow Fenrir Greyback to have a dark mark or be a true Death Eater, many Werewolves and Giants ally themselves with Voldemort's army.
Umbridge does not call him 'The Dark Lord' as most, if not all, Death Eaters do.
There is no evidence that she ever got a Dark Mark. Surely in the movie she did not have one.
There is no evidence that her opinions or ideas changed from Order of the Phoenix to Deathly Hallows. The Ministry has though, and therefore Umbridge fits much better with the new Ministry views.
She is not present in the graveyard scene or Malfoy Mansion scene, nor does she ever play a part in Voldemort's schemes (other than by accident, of course).
That being said, Lupin says in Deathly Hallows:
"A mixture; but to all intents and purposes they're the same thing now. (pg. 206)"