If you can give me a temp admin account, I can make a slight change that can do exactly that.
After the change, a simple change to the shortcode will do it. Something like this:
[connections image=logo image_fallback=siteshot]
The only downside would be if there is no logo and no website for the entry, the placeholder block will not be there because there would be no fallback for the fallback. Hope that makes sense.