Fog with Semi-transparent Pixels, is it possible?

As you may know, SpriteRenderers and Fog don't work that great together.

I'd like to know if it's possible with a shader to keep the alpha detail while making sure it's not visible in the fog. The first image is without alpha cutoff, the second image is with it on.

Notice the lost semi-transparent detail around the edges. I was wondering if there was a way to have a mix of both? (keep semi-transparent pixels but stop the fog turning them white)