No. The autopsy case study found with cycle threshold of 45 the presence of viral RNA (not the spike protein) in many organs. The study is evidence that Pfizer's shot induces a mild immune response.

From the study:

A previously symptomless 86-year-old man received the first dose of the BNT162b2 mRNA COVID-19 vaccine. He died 4 weeks later from acute renal and respiratory failure...SARS-CoV-2 cycle threshold values ([the negative cut-off value was Ct >45)] [were found] in all organs examined (oropharynx, olfactory mucosa, trachea, lungs, heart, kidney and cerebrum)...We demonstrated viral RNA in nearly all organs examined except for the liver and the olfactory bulb.

We suggest that a single treatment with BNT162b2 RNA vaccine elicited significant immunogenicity, as reflected in the reported spike protein-based neutralizing IgG serum values. From the weeks before vaccination, through vaccination (day 1), to shortly before death (day 24), the patient was free of any clinical symptoms typically ascribed to COVID-19...Because our patient died approximately 2 days after his first positive SARS-CoV-2 test result, we suppose that the molecular mapping data reflects an early stage of viral infection. An early stage of infection might also explain why different regions such as the olfactory bulb and liver were not (yet) affected by systemic viral spread.

Our findings are in line with previous evidence from animal models that immunization against SARS-CoV-2 by vaccination appeared to reduce the severity of pathogenesis, especially with regard to severe lung disease, while viral RNA persisted in nasal swabs...In summary, the results of our autopsy case study in a patient with mRNA vaccine confirm the view that by first dose of vaccination against SARS-CoV-2 immunogenicity can already be induced, while sterile immunity is not adequately developed.