The easier critical argument is in the answer of "yes." Horatio, Hamlet's dearest friend, is lifted up as storyteller in his declaration of truth to Denmark, from which there is no longer "something rotten" in this state. In addition, the noble character of Fortinbras (and one without a tragic flaw), is left to lead the country. Everything is well, . . . finally. This would make sense in regards to the definition of tragedy, part of which dileniates a note of hope at the end.
The more difficult, and yet simpler, argument is in the answer of "no." Hamlet, our tragic hero, is dead. Hamlet, who we have commiserated with through the entire play, no longer exists in Denmark. Likewise, Hamlet's whole family and even dear Ophelia die as well. This leaves us knowing, as an audience, that inaction is unacceptable, . . . and that incest is best avoided. Apart from death, however, this argument is harder to prove and rarely reads between the lines.
Fortinbras becomes the King, and he does mention how remarkable and honorable young Hamlet was. Hamlet also does convince Horatio not to drink the poison so that he would be able to tell the story from Hamlet's private point of view since he was Hamlet's closest friend.
Despite the fact that, as with any Shakespearean tragedy, a majority of major characters die by the end of the play, there are arguable positives that also come from the ending of "Hamlet." For instance, Hamlet asks Horatio to tell his story, so finally the truth will come out in the kingdom of Denmark, which is pretty important considering the entire play has been shrouded in deceit, which has been a main cause for each of the deaths. Also, Hamlet tosses his favor to young Fortinbras to succeed to Denmark's throne, which could also be a positive since Hamlet has so much respect and admiration for this character, a man of action.