Not sure I never personally did the get killright assigned right before the pew pew, just know how the system works. But it is possible there is such a delay, but not sure. You can test it on an alt or with a friend I guess to make sure.
For the record what I have personal experience with is activating a public killright (earned from my alt, details here if interested: ★ Headhunters' public killright office ☠️) just before the pew pew (the lock and scram about to land) to eliminate the chance of the target escaping before I can tackle it.