No, but you could guarantee that he wouldn't be killed due to improper care. Death by natural causes (ex. becoming snake food) is generally more accepted than a death caused by human intervention.
He's a predator, not a scavenger, so don't bother with anything dead or not moving. If he's really tiny you need a steady supply of fruit flies and/or pinhead crickets as Cheri mentioned. Have you read the care article I linked to yet? It deals with all life stages of Gray treefrogs and can be applied to your dude.