Unless you are not trying to compile you question from other questions, just to have chance to be upvoted, this is acceptable by all means.
Someone who has asked the question is by definition a person who seeks for information he currently felt the lack of. Someone who answered the question, and that question had been accepted, is definitely well-willing person, who had provided some useful information.
But this does not automatically means that his answer is the best one.
It is always good if somebody will provide some additional information (or another point of view on the issue).
As for the part "do people look", be pretty sure they do. If you'll inspect the set of highly up-voted questions, you will mention that most of them have quite often a bunch of high-voted answers. It's not that rare that some answer has more votes than accepted one.
Besides, do not forget that any answer, even perfect one, can just become outdated or even contrary to current practices.