greeting('Hello', 'Good Looking'); # prints immediately greeting('Woah'); # Waits ... greeting('Nelly'); # prints now that it has both arguments

I don't think so. greeting('Woah') would, as far as I can tell, yield a new function that takes a single argument, so it would have to be used in a context where that other argument will appear.

I'd expect it to be analagous to greeting('Whoa')->('Nelly');