Plenty of people who are infected have received vaccinations, since so many infections are asymptomatic. It's inevitable, because they don't test people before their vaccine appointment. It's not adding to the amount of virus you have. It does increase the amount of viral antigen you have, so it gives you a stronger immune response. Covid-19 induces a weak immune response in some people, at least in terms of antibody production. That's probably because they cleared the viral antigen before the adaptive immune system could get involved. It is a bit slower than the innate immune system. Like pretty much everything the body does, there are negative feedback signals so the process can be shut down when it's no longer needed. If there is no viral antigen when antibody production is ready, no antibodies. Production of antigen-specific antibodies is called "seroconversion", and lots of SARS-COV2 infected people are "sero-negative". Including me.
