Sorry for being so jaded, but no they won't. I battled with Tesla and 3 different service centers for 6+ months on this issue. I was even told this hilarious soundbit:
"The screen's brightness level generates heat, meaning the screen is still a mileage related item"
I was so floored by that response I about lost my cool when I replied that "Tesla's feature auto adjusts the screen brightness for me, and has for awhile now".
If they do break down and decide to cover this outside the normal warranty, what will they do for all those they charged 3-5k to replace the screen?
Ironically this means the problem gets worse as the situation gets sunnier. It's sunny (and hot) - the car responds "let's turn up the brightness" and generate more heat - melt the glue extra fast!