If I receive an "honorary doctorate" from a reputable university, would it be wrong to refer to myself as "doctor"?
This wikipedia article has a lot of good information about honorary degrees (especially, honorary doctorates).  The major takeaway is that a recipient of an honorary doctorate should not try to mislead people into thinking that he has an earned doctoral degree.  An honorary doctorate is really an award and not a degree, so it would be, well, honorable to take pains to describe it accurately.  Thus you should probably not describe yourself as "Dr. Horsehair" except in a context in which the honorary degree has already explicitly been discussed and is relevant (e.g. at a ceremony at the institution which awarded the doctorate).

Listing yourself as having a PhD when submitting an academic paper seems willfully misleading and thus unethical.  Moreover you should not at all neglect the possibility that an editor or referee will do some quick internet search and discover that your PhD is not a "real one": this would not reflect well on you.  

A PhD has a very specific meaning within the academic community: it is an academic credential.  Academics take academic credentials very seriously, and the PhD is one of the most serious academic credentials, so you should expect academics to take that credential very seriously.  Appearing to flout -- or even worse, not understand the significance of -- academic credentials is one of the worst things that a would-be academic researcher could do.  On the other hand, a PhD is "just a credential": it is not a badge of honor, a sign of superior intelligence, greater worth or anything like that.  Most lifelong academics have met PhD holders whose academic skills are wholly unimpressive as well as non-PhD holders (of both the "not-yet" and the "never" varieties) who are brilliant and academically accomplished.  Portraying yourself as having a PhD is not going to elevate you within the academic community in any fundamental way (but, as I said above, a discovery that you do not have the earned PhD that you implied you did may well be held against you).  Just be honest and keep your head up.