(Not a Teacher)
In your sentence, you are asking what the other person thinks, not whether the guy will be back before noon, hence "do you?".
Also, I want to note that the "do you?" at the end of this sentence sounds a little sarcastic (as if you said, "Did you really think he'd be back before noon? You're more gullible than I thought!). You'd have to be careful with your intonation here.
We don't typically put "I don't think" at the end of a sentence.
"I think" comes at the end of the sentence to emphasize that we don't know something for sure. "As far as I know" serves the same purpose.