Iza, nope. I am talking about dynamic stability, what we need to have a nice stable a/c.
In the example above, you have it trimmed for 150 knots. Then without trimming, push the stick to 170. With the cg behind the cl, it will diverge and start accelerating well past the 170. Until parts start coming off, etc. With positive stability it would return (sooner or later) to 150. But only with the tail providing a down force.

Ever fly a plane with the cg further back than was comfortable? Gets all loose right? Well, imagine it even further back. It becomes impossible. That is what it would be like with the stab providing lift. You would get some great efficiency on your way though.