Natural corks are porous, which means they would let small amounts of oxygen into the bottle over time. Not only that, but their porous nature also means they won't form a vacuum seal when you pasteurize your bottled sake. Therefore, natural corks are not a good option for sealing sake bottles, especially for long term storage (i.e. more than 6 months).
Synthetic corks are another matter. They are not porous, so they don't have the oxygen permeability problems that natural corks do. There is still some risk that they could get sucked into the bottle by vacuum when sealing hot sake bottles, but synthetic T corks would avoid that issue.