In nu trek its nu kirk etal who go back in time to 1930 thru the guardian ; 1986 to get the whales; 1967 to meet Gary Seven. Etc.
No to all three.
From the point of view of those periods in time, "prime Trek" is still a possible future, therefore Kirk Prime could still arrive from it. Remember, the prime timeline has not been erased
Indeed, it is possible for characters from EITHER timeline to travel back to those periods, or indeed any period before 2233 - since both timelines are possible, and coexist side by side. Kirk Prime and nuKirk could even meet!