I think that the other answers do not quite answer the question that was asked. My answer is no, it is not cheating to turn in a homework assignment that cites a website like Math.SE. (This is assuming that you put quotation marks around any text that you copy; otherwise it could still be plagiarism.)
Of course it would be a good idea to ask the professor beforehand whether this is allowed, but failure to do so would not constitute cheating any more than attempting to turn in a homework assignment late without first determining whether this was allowed would constitute cheating. As long as the student makes it clear that the homework uses outside sources (or was turned in late,) the professor has the choice to accept the homework or not according to his or her policy.
Keep in mind that if citing outside sources in your homework is a violation of the professor's policy, then the penalty could be significant (just as for failing to turn in the homework on time.) However, it is still not something that the professor could reasonably report to the university administration as cheating, nor is it something that a reasonable university would consider to be cheating.
According to the Merriam-Webster online dictionary, the relevant definitions of "cheating" are
1a: to practice fraud or trickery
2b: to violate rules dishonestly.
In both definitions, dishonesty is a crucial element (and one which the OP has explicitly ruled out.) In fact cheating, plagiarism, falsification of data, etc., are often collectively termed "academic dishonesty," making this condition explicit.