interstate purchase of unregistered

Yes, an Unregistered person can make interstate purchase. However he cannot make any interstate sale/ supply.

It is mandatory for a person making interstate sale/ supply to get GST registration irrespective of threshhold limit.

i.e even if turnover is below Rs 20 Lacs ( or as the case may be) and there is Interstate supply (Sale) of goods by a person he must get GST registration.