Just a random thought, What if I wanted to showcase a responsive webdesign not by resizing the browser window, but actually loading the responsive site in an IFRAME having the s
What you propose should work, assuming you don't have anything else screwy like the child intentionally grabbing CSS from the parent etc.
Something like Firefox's responsive design view is designed for exactly what you are talking about too:
https://developer.mozilla.org/en-US/docs/Tools/Responsive_Design_View
It's not hard to use, but I guess harder than just telling your client to "click here".