Actually, I'm pretty sure that is the first time I've seen that question.
While I don't see any technical reason why not, I've never heard of an app (or pair of apps probably) that would do this. Pretty much all the results when you search for nanny cam are about using the iPad as the monitor, not the camera.
The only apps I've heard of that work somewhat this way are for viewing the iPhone camera on the iPad; mostly written for the iPad 1. Its been updated somewhat since, and the description appears to suggest you could do it the other way around. The apps names are Camera-A for the iPad and Camera-B for the iPhone.
At any rate, you're only risking 99 cents to find out.
Matter of fact, I can see some other uses I might put this too, so I think I'll go get it and try things out. I'll come back to this no latter than tomorrow and let you know if it can be done with these apps, and how well it works.