That previous potential instance (I confess to not remembering Discovery well) notwithstanding (and it's possible that he was simply wrong in that example), I don't think the show has portrayed Pike's predestination as "nothing else CAN happen to him" (indeed, the end of S1 explicitly suggests otherwise), but rather, "he must not diverge from his predestined course." It's not an excuse for Pike to do stupid things. Time isn't going to protect him. He can still be killed if he does something stupid that he wouldn't have done before believing that he was predestined to live a few more years.
(Incidentally, does Pike know that he's supposed to live beyond the accident, and/or know about his Talosian destiny afterwards, or does he just know that he's destined to HAVE that accident?)