With mRNA vaccines, how far does the vaccine travel in the bloodstream before the mRNA finds its way into a host cell? Is it possible, for example, that a vacci

With mRNA vaccines, how far does the vaccine travel in the bloodstream before the mRNA finds its way into a host cell? Is it possible, for example, that a vaccine shot delivered to the shoulder can circulate around till it reaches sperm and egg cells and gets into one of them? Does a DNA vaccine have properties that change how far it can travel? Or any known mechanisms that will prevent a possible DNA alteration happening in the sperm or egg cells where it might land?