Asking whether or not Socrates was a hero takes him out of his culture and transplants him to the early 21st century. As a historian I can say strongly that it is a false question. A far better question would ask if he was a hero in his own culture and the answer is “no” but not because he was condemned by a jury of Athenians.
The concept of “hero” is radically in the classical than today’s modern image of a hero. Today a hero is someone who sacrifices or is willing to sacrifice him/herself for others. Socrates was not willing to do that, indeed the charges against him had little to do with him and much to do with some of the choices formers students had made when Sparta briefly controlled Athens. True, Socrates did fight and may had been a fine hoplite but so were many citizens in the 5th century. The sacrifice he seemed to make regularly was the well-fare of his wife and sons whom reportedly suffered because he preferred to talk with other men about political, social, and philosophical matters than earn a living. In our world he might be seen more as a selfish intellectual than any sort of hero.
In the classical world a hero was a particular type of character and Socrates qualifies as a hero on none of these accounts. First heroes have godly connections, usually through one parent or through a direct line of descent from the gods. Socrates and his students never claimed this for him.
Secondly classical heroes lived outside the norms and rules of their society. They could get away with outrageous behavior though not always without penalty. They were often immoral and out of control when compared to other morals. Again the image we have a Socrates is a man of moderation in most of his actions.
Third, classical heroes are targeted by the gods and must survive their attacks. Yes, they are also aid by other gods, usually allies of their parent or ancestor, but their enemies constantly throw hardship in their paths be they in the form of monsters or petty tyrants or insanity. Socrates seems to have been targeted primarily by other philosophers and playwrights during his lifetime until the very end when a restored democracy took him to task for the actions of his former students.
Fourth, classical heroes over come these attacks and their exploits survive in numerous legends. Socrates’s students, especially Plato and Xenophon, left behind dialogs they claimed were discussions he had over his lifetime. Other legends, tales that people might share as an example of heroic behavior or exploits do not seem to survive for Socrates.
Fifth, classical heroes have cults established for them after their deaths. By surviving for years the attacks from gods, by being part divine themselves, and for their outrageous behavior, later generations literally worshiped them. There is no evidence that such religious or cult devotion was applied to Socrates.
By all accounts then the classical world would not have considered Socrates a hero. By out own definitions of hero I doubt that we would as well.
