Is possession of a Permanent Account Number (PAN) mandatory for obtaining a Registration?

Yes. As per Section 25(6) of the CGST/SGST Act every person shall have a Permanent Account Number issued under the Income Tax Act,1961(43 of 1961) in order to be eligible for grant of registration.
However as per the proviso to the aforesaid section 25(6), a person required to deduct tax under Section 51, may have, in lieu of a PAN, a Tax Deduction and Collection Account Number issued under the said Income Tax Act, in order to be eligible for grant of registration.

Also, as per Section 25(7) PAN is not mandatory for a non-resident taxable person who may be granted registration on the basis of any other document as maybe prescribed.