Is it possible to get un-permabanned if behavior on a new account improves for a long period of time

nope

They already answered, but I'll elaborate. Riot used to have a program in which they would hand pick and interview permabanned players, then if they could get a new account to level 20 and show they reformed they'd get their account back. However, even after all the work Riot went through 95% of those players still went right back to their toxic behavior and got permabanned again. The program was scrapped due to players proving that they'd almost assuredly go back to ruining games if they were put back in the population, doing so for hundreds or even thousands of other players before they were stopped.

No. If you get permabanned, you don't deserve to play.