No, I do not think so. In OS X, windows (and thereby NSWindow s) are composed by a window server and have their own buffers. Theyre essentially OpenGL quadrants, and the drawing is done in texture (this is a simplification, but it basically works).
You will not explain in your question why you are using a child window (unlike, for example, with support for a layer or even a simple NSView ); often you may not have to use child windows at all, which seems to be the easiest solution to your problem in this case.
(Note that if you came from a Windows background, Cocoa expects you to use views rather than windows for most purposes, in a typical application you only need to use windows at the top level of the interface hierarchy.)