Yes,He showed up with empty boxes.

The sentence is fine, nothing wrong with it grammatically. I think it might be clearer though if stated like this: A delivery guy turned up but without any packages. So why did the delivery man turn up? It's an interesting sentence because it leaves the listener wanting to know more, there is a sense of mystery. It sounds like the beginning of an interesting story.

There aren't any grammatical errors, but the meaning isn't clear.