I'm not sure I know the answer to this. I think I do, but I thought I'd ask as I'm not positive of the answer.
What I know:
Even the best lenses perform better in the center of the projected image circle over the sensor than at the edge (some far better than others, yes). This difference is alway more evident wide open regardless of lens (you can see in my sig I do have one of the rare ones that's close to the same @ any aperture; no need to diverge the thread on this point

).
What I'm wondering:
So given how light enters a lens and that the light rays that project in line with the FOV of the lens project onto the sensor, when I put a TC on a lens, is it true that some center x% of the image circle (value of x% based on the magnification of the TC) is magnified to cover the sensor, thus pushing the reduced 'edge' performance of the image circle farther out and off the sensor?
And if I have a lens that has fantastic center performance but only "ok" edge performance when wide open, am I making better use of the superior center resolution of a lens when I have a TC is attached? For an example... So, if a lens's front element is 50mm diameter, and I use a 1.5x TC, is it that only the light that passes through the center 33.3mm of that front element making it to the sensor? (yes, I know a full frame lens's edge is already lost on a digital sensor; i.e. the cropping factor. only citing these numbers as a talking point example)
Thanx much for your informed replies,
-steve