To my knowledge, it will only act differently if you go to one extreme or the other. And usually, that will be the result of bringing on another issue, most likely contact with the shelf or strike plate. The closer cut to center the strike plate is, the less of an effect it will have, but it will still have an effect!
Your initial thinking is the most logical (and was my own at one time), but there are more variables to consider than just the obvious. Your diagram is a good illustration of one of those variables. Another important factor is the preload of the limbs.
By shortening your string (increasing brace height), you are increasing the preload of the limbs and creating more string tension. This means that the limbs are already bent more at rest than with a lower brace (moving the center of the working limb length). So they will have more tension (or strength to return to brace), and less string slack and travel. I'm not sure about increasing peak draw weight with a higher brace, as your draw length does not change, but I have not confirmed nor denied this with a scale. I know that a lower brace will generally feel smoother to draw, but again, there are many factors that affect that as well.
It is generally accepted that a higher brace equals a more forgiving bow, but the most forgiving a bow can be is when it is shooting a perfectly tuned arrow!
Yes, you will sacrifice a couple fps by increasing brace, but in my experience, it's not enough to alter your effective range. Again, a perfectly flying arrow will perform better than one that wobbles or kicks even if it is slightly faster.