Everything I have seen shows that vaccination provides an increase in circulating neutralizing antibodies, even in COVID-19 recovered people, which would be critical for stopping the initial infection - and allowing you to test positive despite a second exposure.
I've posted this a lot but look at fig 1 here.
https://www.nature.com/articles/s41591-021-01325-6
Hocker really should get vaxxed if he wants to minimize his chance of testing positive.
Also I there seems to be debate that "natural" immunity is all the effect for population level immunity:
https://www.thelancet.com/article/S0140-6736(21)00183-5/fulltext
Hocker is probably fine not vaccinated but a positive test ends his Olympics... which he risk it?