No, I mean, the immunity achieved after fighting off infection, which includes antibodies in the blood stream for a period of time, and, as far as we can tell, long-lasting, probably permanent, T- and B-cell memory.
And post-infection immunity is achieved not just by production of s-protein antibodies, but antibodies to proteins of the membrane, the nucleocapsid, and the envelope of the virus.
By "natural immunity", you mean, "getting infected"?