Is it possible to "Blur a Transparent Background" in Adobe After Effects? I am a beginner to Adobe After Effects and Sony Vegas Pro, so forgive me for a lack of a better term.

I am trying to create an Adobe After Effects composition. I want the composition to be transparent with a blur effect. I want to add this blur effect to be in such a way that upon exporting it to an .avi file, I can add this .avi file to a Sony Vegas Project, and the .avi file will blur any layers underneath it.

To illustrate, suppose I have the following Sony Vegas Project:



I want to create an after effects composition such that I can make the image look something like this:



However, I don't want to render the composition with the image in it. I want to render it as an .avi file such that I can apply the blur effect to any arbitrary image, or even video files.



Is this possible? My intuition tells me no, but I'm asking in case there is a way.
It's not possible. A generic blur effect relies on a function which smooths out pixel values within a specified radius. A mask combines the value of a pixel in the top layer with the pixel of the layer beneath, modulated by the corresponding alpha value of that pixel in the top layer.

So, in short a blur is a 'lateral' function, whereas layer compositing is a 'depth' function.