Using TGCocoa

I am a little confused as to how I use TGCocoa in my Mac application. I was looking at the iOS example, and they are able to call the iOS equivalent:

How would I do something similar for a Cocoa based app?

You’re not supposed to use TGCocoa directly, it’s a low-level interface that essentially implements X11-like API with Apple’s Cocoa/Foundation/QuartzGraphics framework, to make ROOT’s GUI work on OS X.
What you need is TCanvas/TPad/ROOT’s GUI and there’s plenty of tutorials, explaining how and what to do.

Can TPad and such be drawn into a standard Cocoa window via NSView?

No, as implemented now - ROOT’s windows/views (of type QuartzWindow/QuartzView inherited from NSWindow/NSView) can have only QuartzWindow/QuartzView as parents (QuartzView as a child).