No. There is nobody to replace him. If they were playing at home and another opener was knocking the door down with massive runs , they may ask some questions of Cook. Away from home, limited options, test record of Cook, he will play the five tests. He would need to drop himself to not play.
England play so many tests now (7 in England during their summer) it’s sort of glossed over how badly out of form he is.
The thing he had was enormous mental application, bat all day stuff, personally he’s lost that.
Even if he gets in against the new ball can’t see him making those big scores atm.