Whether the Department through the proper officer, can suo-moto proceed with registration of a Person under the Act

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

(ICAI FAQ PUBLICATIONS 06-09-2017 REGISTRATION: FAQ NO. 8)