Due to the death of Annabel Lee, is it possible that Edgar Allen Poe's death was a result and attempt from the pain of losing her?
He was surrounded by death from childhood; these deaths, I'm sure, all had a cumulative effect, and all, in their own way, led to his poor lifestyle choices. He suffered from depression (allegedly at least, but how can one think differently after reading his works!) and also was an alleged alcoholic and drug abuser. Poe was found "unresponsive" in a gutter in a city that he really was not expected to be in. His death is believed to be a result, even if an indirect result, of these choices.
So sure, thereby one can conclude that his wife's death (Annabel Lee was not real) in real life continued to add to his depression and abuse, and in turn, caused his death.
Poe had lots and lots of very deep-seated issues--as a result he died young and basically penniless!
Just a word of caution about superimposing the incidents in a fictional work--poem, short story, or novel--over the life of the author. It's true the author's life experiences, emotions, and circumstance all combine to create an author's point of view. What may or may not be true is that he applies those directly to his work. The speaker of the poem may or may not be the author. In this work, it's clear Poe has experienced loss and knows what it's like to grieve. That's really all we can know for sure, unless we have some commentary from Poe himself.
We'll never know the answer to this question. Annabel Lee was not a real person but was based on Poe's wife, Virginia Clemm. He was deeply in love with her and greatly mourned her death. Historians tell us that Poe died from complications of alcoholism. Perhaps his beloved wife's death caused him to drink so much, so in that sense you could say that her death eventually led to his death. Unless someone finds a lost journal in some dark, dusty attic, all we can do is speculate.