Yes, the GST department can send notice to an unregistered person if it believes that the business was supposed to be registered under GST and tax loss to the state.
Section 63 of CGST Act, empowers GST department to assess the taxable income and tax the person.
63. Assessment of unregistered persons.- Notwithstanding anything to the contrary
contained in section 73 or section 74, where a taxable person fails to obtain registration even though
liable to do so or whose registration has been cancelled under sub-section (2) of section 29 but who
was liable to pay tax, the proper officer may proceed to assess the tax liability of such taxable person
to the best of his judgement for the relevant tax periods and issue an assessment order within a
period of five years from the date specified under section 44 for furnishing of the annual return for
the financial year to which the tax not paid relates:
Provided that no such assessment order shall be passed without giving the person an
opportunity of being heard.
As you can see the notice was sent as per section 63 of the Act. You should produce the required documents to department and based on these records, department will pass the order after giving you time to respond.