Whether the Department through the proper officer, can suo-moto proceed to register of a Person under this Act?

Yes. In terms of sub-section (8) of Section 25, where a person who is liable to be registered under this Act fails to obtain registration, the proper officer may, without prejudice to any action which may be taken under this Act, or under any other law for the time being in force, proceed to register such person in the manner as is prescribed in the Registration rules.