Is a bank employee considered to be a central government employee?

No, whether they are bank employees or employees of the Supreme Court or any other courts, Parliament, Central Govt undertakings such as EPFO, LIC, Autonomous Bodies, etc are not considered to be Central Govt employees. No benefits of any kind for him are  given to them in an Staff Selection Commission (SSC) exam or the posts through it’s exams.

And therefore, they cannot seek age relaxation that is available to the Central Govt Employees in the Staff Selection Commission (SSC) exams or the exams conducted by the UPSC or any other recruiting agency/board meant for recruitment of candidates in the Central Government.