Not necessarily, if they kill their host after a couple of weeks they will spread very effectively indeed, the longer the asymptomatic spread period the better for a virus' chances of moving on to a fresh host undetected. During symptomatic spreading there is at least a warning that someone might be contagious so this is a harder way to spread. And for some viruses it is even possible to spread after the host has died. What happens to the host itself after the virus has spread doesn't really matter. If a host dies before spreading and the virus can't be spread from the corpse then that will work against the virus.