Is Willy a modern hero?
According to Arthur Miller, Willy Loman is a modern tragic hero. In his essay "Tragedy and the Modern Man" Miller describes a tragic hero as one who is at the point in their life where they are in fear of losing their sense of who they are. Willy has lived his life with the illusion of being "well liked." In the play, he is coming to terms with the reality of his life and the fact that everything that he has lived for is but an illusion.
In his essay Miller makes the point that a modern tragic hero does not have to be of noble birth or necessarily have any of the qualities that Aristotle lays out in "Poetics."
It would be worthwhile to read Miller's essay as it helps to put in perspective Willy's situation.
In my opinion, no, Willy is not a hero, modern or otherwise. In fact, he is the antithesis of a hero.
In broad terms, a hero is one who overcomes obstacles and wins a better life for himself, his family, or his community. Willy does none of these things.
His dreams of being well-liked fall flat; even at his funeral, no one is present save his immediate family. His boys are trapped in a never-ending adolescence, his wife must worry constantly about the bills and his state of mind.
Though we feel immense pity and sometimes empathy for Willy, it is not possible to understand him as a hero in any sense of the word.