Usually my answer to "would be possible?" questions is yes.
Could you compare it to something you come across in every day life?
Surfaces are a good place to start, although it could be more straight forward to make a shader.
I'm assuming your going for something similar to a tinted glass window (if not you may need to separate out the overall effect you want to achieve into different parts)
Just remember the application_surface is the default surface that everything gets drawn to.
You can copy the part of the application_surface where you want the effect and save it to a new surface.
Once you have that you can draw the surface to itself a few times with a lower alpha and small offsets to give it a nice blur.
Draw the surface in the room then draw a transparent window sprite on top and you have a window that blurs whatever gets drawn behind it!
It sounds like your going for a heat wave refraction type effect. I'd probably start with some basic surface effect tutorials.
So I guess that answers your question. Let us know what you end up trying and how it goes since you already have a thread open.