Yes, an episode of cannibalism involving a cabin boy named Richard Parker did happen 46 years after Poe wrote the novel.
The shipwreck is that of the English yatch Mignonette, which became a famous criminal case (R v Dudley and Stephens).
As the Wikipedia page for the case points out:
The case is familiar among lawyers in the common law jurisdictions — that is, England and many, though not all, former British territories — and is universally studied by law students in such jurisdictions. Simpson observed that, though many murderers have become household names in Britain, the case is surprisingly unfamiliar to the public at large.
It became better known in 1974 when Arthur Koestler ran a competition in The Sunday Times, in which readers were invited to send in the most striking coincidence they knew of. The winning entry pointed out that in Edgar Allan Poe's novel The Narrative of Arthur Gordon Pym of Nantucket, published in 1838, decades before the Mignonette sank, four men are cast adrift on their capsized ship and draw lots to decide which of them should be sacrificed as food for the other three. The loser was the sailor who had proposed the idea: the character's name was Richard Parker.
Richard Parker is the name of several people in real life and fiction who became shipwrecked, with some of them subsequently being cannibalised by their fellow seamen. Writer Yann Martel in his 2001 novel Life of Pi picked up on these occurrences, surmising "So many Richard Parkers had to mean something", and included a shipwrecked Bengal tiger called "Richard Parker" in the book.
So, Poe did predict the future, in the sense that he (sort of) did write about something before it happened.
However, there seems to be an "implied" claim, that Poe did that using some sort of psychic powers, which needs to be addressed as well. Since there is no scientific proof that psychic abilities exist (see Do psychic abilities work? and references within), this would be quite an extraordinary claim, which would be much interesting, but would also require extraordinary evidence to support it. Alas, as for many psychic powers described so far, the most likely explanation is that it was just a coincidence; this is reinforced by the fact:
The coincidence stops at the fact that the cabin boy was cannibalized after a shipwreck. The details of the death of the boy are different:
in the novel Richard Parker proposes to draw lots and is killed as a consequence, while the real Richard Parker was sick (possibly in a coma?) when he was killed. Also the names of the other people on the boat are different. If Poe were able to see the future, he would have "seen" the correct names. The obvious counter-answer to this is that he couldn't see the future quite clearly, but then the onus of proof is on whoever says he was a psychic to prove this... (this becomes very quickly a "there is a dragon in my garage" argument).
Richard Parker is a common name, shared by various well known people as well as generally common in the general population
Shipwrecks were fairly common at the time, often even several per month (varies year by year, possibly because not all were recorded?).
In summary, as for many other supposedly psychic/supernatural events, there is a much simpler explanation.