Does any aspect of a Hero Mode game affect the street pass battle feature of Link Between Worlds?
It doesn't matter, whether the file is in Hero Mode or not. You can receive Shadow Links from a normal game in a Hero Mode file and vice versa. Only your name, equipment and medal count will be transmitted. However, the Shadow Links will deal four times the damage in Hero Mode. A purple potion for example causes 32 hearts of damage on you... You will only deal normal damage on them, so be prepared.