It depends. It must be pretty well designed to work. And even in pretty good games, like RE4, the mission suck but the game is good enough to compensate it.
I don't consider TLOU a escort mission game. Ok, you are theorically escorting Ellie, but she is invisible to enemies and only very rarely she will be attacked, and even then you have almost 2 minutes to save her. You can drink a damn coffee and return in time.