Yes you can.
The Generation VI version of the Pokémon Global Link launched on October 12, 2013. Players who register on the Pokémon X and Y Global Link with the same username as on the Pokémon Black, White, Black 2 and White 2 Global Link will be able to carry over certain achievements and records.
Source: Here and I have an PGL Account
For the Generation VI Global Link features click here.
Hope I helped :)