How can I insert a Google Analytics image in a Facebook status to help facilitate good reach of important status posts?
I apologize for wrongly phrasing the question
Question implies embed code ( converted into tracking image ) to understand reach free status updates
I'm not sure if this was badly edited, but you can start by rephrasing the question so it makes sense. Did you mean to write "script" instead of "image"? There's no such thing as Google Analytics image.
So if you did mean "script", then that's not possible. The best you can do is have analytics on the page you link to, then look at social referral traffic to judge the effect.
To improve reach, you can pay Facebook to promote a post.