Just like English "will" or "would", -겠- frequently means assumption:
좀 있으면 비 오겠다 = It may rain soon.
아까 그 기차 탔으면 벌써 도착했겠다. = If we had taken the train, we would have arrived by now.
So, "빈손으로 왔겠다" would mean "[He] would have come empty-handed."
Now, the tricky part: "내가 빈손으로 왔겠어?" would be "would I have come empty-handed?"
It works basically in the same way in Korean as in English, in that it questions the assumption of the listener:
Do you think I would have come empty-handed?
Also, 설마 is used to indicate "there's no chance" and makes sure that the whole question is understood as rhetorical (instead of a genuine question). So, "설마 내가 빈손으로 왔겠어?" is something like:
Come on, you don't think I would have come empty-handed, do you?