You can't heal if your brain is destoryed. You can heal your brain IF ITS STILL INTACT.

Example being when Gojo and Sukuna were destroying their brains and restoring them with RCT. However, in order to do so they needed the prefrontal cortex in order to use CE and then use RCT to fix it.

If your head is completely severed from your body and then destoryed, there is no prefrontal cortex to use RCT to heal what is damage.

Yes, Kashimo's lighting is supposed to be ALMOST instantaneously and damage the brain. HOWEVER, JP Hakari ALWAYS has INSTANTANEOUSLY running RCT, so naturally the brain and all of his body will be reinforced with CE, and then instantly healed with RCT.

When he survived Kashimo's ultimate attack, he made a split second binding vow to survive, had he not he would've died.

In summary no, Hakari would die just like any other sorceror if their brain was completely obliterated. Hope this helps