Comedy, especially satire, certainly does not end happily. While satire does not follow the path of tragedy with its noble protagonist and tragic end, it does have the similarity of pointing to the flaws of human beings.  And, as tragedy often does, satire criticizes individuals, ideals, institutions or society. And, so, it is possible for satire to achieve some of the same ends as tragedy.

Aristotle's tragic hero needed to possess hamartia (tragic flaw). This flaw was the main thing which led to the hero's downfall. While the downfall was not always the hero's fault (think the witches and Lady Macbeth), the fact that they possessed the flaw in the first place allowed others to manipulate them.

Aristotle's tragic hero had to have a downfall that inspired pity on the part of the audience. In the process, the audience was supposed to experience "catharsis," the interesting effect of watching someone else struggle through their problems. I don't think a comedy could fulfill these requirements. The audience wouldn't feel the pity in a comedy that is required to produce catharsis.

I may be missing your point, but the intent of comedy as opposed to Aristotle's tragedy (defined) is completely different. With Greek comedy (comedy-drama, etc,.), the intent was to entertain. Whereas the tragedy would often teach a lesson, it was about a great person (often, but not always, a man) who experienced a drastic "reversal" (peripeteia) of luck. Where comedy had a happy ending, the tragedy ended in death. Comedy was supposed to entertain and would not be about a great (accomplished) person, but would be about the lower classes, while Aristotle's perception of tragedy referred to the tragic hero (who was a "great" or accomplished, highly regarded man—not a commoner).

If you are asking whether comedy and tragedy could both "entertain" an audience, I would say yes, but that would depend on a very general definition of entertainment. Both would be diverting, however I see entertainment as something that brings pleasure. A tragedy would be diverting as well, but I believe it would require some reflection, and would certainly not be uplifting as a comedy would be. 

I think that Aristotle would see that each would have a separate purpose and would not provide the same effect.