You cannot delete immediately after death, however you CAN quit.
Try it sometime, just don't hit delete more than once 
You can delete immediately after death, both player and mobdeath. Trust me. I did it today, and various times in the past where I've rolled characters to test something, found myself unable to delete after recently fighting, so killing BIG MOB then deleting right after. 
Mob's punch *** DEMOLISHES *** you!
You have been KILLED!!
As the cold chill of death descends upon you Chayesh grants you yet another chance.
You have been granted a temporary sanctuary as an invincible ghost.
As long as you don't attack anything.
delete
Type delete again to confirm this command.
WARNING: this command is irreversible.
Typing delete with an argument will undo delete status.
delete
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Just tried it now to make sure.
Dey