Actually, to be technically correct (according to Aristolian rubrics) the answer is 'no'. Aristolian tragediecs have three unifying elements: action, place and the time(usually short span of time...like one day). Therefore, in order to conform to Aristotle's idea of a tragedy, Othello would have to happen in a day, have no subplots at all, and happen in one location.
As to the tragic hero question.....
Aristotle stated that a tragic hero must:
A tragic hero must be a person of high status; an individual that an audience should look up to and admire
A tragic hero must be, essentially, ‘good’
A tragic hero cannot have committed any evil or catastrophic deed with intent
A tragic hero must have a fatal weakness and it is this flaw which causes him to ‘accidentally’ commit the aforementioned deed
Othello was not a man of high status (at least at the beginning and even after he becomes King he is still viewed by most as being somehow 'less'). And, he is bascially a decent person. This is where the comparison has to end, however, with Aristototle's definition.
Othello does NOT cause an injury in ignorance (no misjudgement or accident). He meant to kill Desdemona. Some argue that his misjudgement was to judge Desdemona wrongly, but even so, he believed that he was killing an unfaithful wife...which shows low character. The tragic flaw is also not up to Aristotle's standards. Many have said that his tragic flaw is jealousy but this is a difficult argument to maintain since jealousy cannot exist on its own...it requires external influence. Rather, he is a victim of the racism and his own insecurity about his position at court.