Any answer to this question would be purely conjecture. We don't have any secular evidence to suggest one way or the other with any certainty.
The mythology spoken of above can be taken or left, depending on what brand of Buddhism you follow. Zen would not, for example, give two shakes about anything The Buddha did after death, if, indeed, it was possible he could. Tibetan Buddhism has a huge mythology built up around things like this, and mystical events that are quite detailed. Pureland Buddhism would tell you you simply can't become enlightened in this lifetime, and that you must say the Mantra of Amitabha Buddha to become enlightened in the Pureland after death.
It all depends on the flavor of ideology you are involved in.
At its core, Buddhism doesn't care. :-)
Now if you are asking this question in an attempt to get at some historical figure you think that Siddhartha may have taught, can you tell us who that might be?