First thought I’d say no, but after thinking about it awhile - I would think that since in any disease the contagion is only transmissible for a certain period of time and not through the entire patient’s illness, at least that is my understanding for a normal infection, I suppose one could take the position that if one has only mild symptoms for a few days they would be less likely to be infectious for the same length of time as
someone getting a full blown 2 week infection. BUT an asymptomatic individual of either party, natural or vaccinated, would be of equal infectious potential.