Yes, she is dead. Either killed by the original assailant(s), or more likely, she survived the assault, and was later killed (as Teddy states) by Leonard himself, in an insulin overdose. Either way she is definitely dead, though she appears alive in the brief fantasy scene which is why that scene has to be imaginary.
At the end of the movie, Leonard successfully, intentionally tricks himself into thinking he has avenged her death by killing Teddy, so a photo of a tatoo stating that is not surprising or contradictory; but it is a logical way for him to remember the event and rest, thus preventing further manipulation from the likes of Teddy and Natalie to achieve their own ends. In reality people are often manipulated by others (though not as blatantly), so this theme of manipulation becomes a metaphor for life in general.