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.