It's perfectly fine to throw around that kind of phrase without ending the sentence or even using a question mark. It just adds emphasis to the statement.
So, you tend to hear it in spoken conversations more often. Something like
I was going to the store, and wouldn't you know it, I saw our old friend Tom
The "wouldn't you know it" is a kind of question, but in context you can tell that the main point this person is trying to get across is that they found an old friend at the store. You wouldn't hear this and think you were actually expected to respond to the embedded question. It's just there to spice up the sentence.
You wouldn't be surprised, would you, if I told you he got too drunk"
It's not really a question, simply a statement, and the embedded "would you?" is just there for emphasis
In british english you might hear "innit" (from "isn't it"), as in
It's a nice day, innit?
But it's been used so much in so many situations that it has partially lost it's strict original meaning of "isn't it?" and become something new (and wonderful):
We’re British, Innit.
I was just joking, innit!
It's become a simple marker of emphasis