If Spock Prime dies in the Alternate Reality, then the same thing will happen that happened to Kirk. What I mean by that, is since Kirk was presumed dead in 2293, he infact survived and reappeard in the 24th century only to actually die again. Kirk is officially announced as dead in the prime universe in 2293. Only Picard knows that Kirk died again.
With Ambassador Spock being listed as dead in the Prime Universe when being transported to the Alternate Reality in 2387, he may die "again" if he dies in the Alternate Reality. However, he is the only member from the Prime Universe who would know. As far as I know, Nero is the only other member from the Prime Reality and he's dead now.
Kirk: 2233-2293 (officially) 2371 (only Picard knows)
Spock: 2230-2387 (officially) 2258 (only Nero knows)
With Ambassador Spock being listed as dead in the Prime Universe when being transported to the Alternate Reality in 2387, he may die "again" if he dies in the Alternate Reality. However, he is the only member from the Prime Universe who would know. As far as I know, Nero is the only other member from the Prime Reality and he's dead now.
Kirk: 2233-2293 (officially) 2371 (only Picard knows)
Spock: 2230-2387 (officially) 2258 (only Nero knows)