At the end of the second Arc of the first season, Kirito was able to access Kayaba's Administrator Account and gained control of ALO's systems. Afterwards, Kayaba appeared and gave Kirito The Seed, a free kernel of the Cardinal System for the creation of new games and allowing players to pass stats between games. This ended up creating The Seed Nexus.
Now I am wondering, since ALO and the Recreated SAO are a part of The Seed Nexus, can Kayaba's Administrator Account go between games? Also