While a virus is not a fully functional living organism, it is not dead because it has the ability to cause its own reproduction in the proper medium. This is what makes it an obligatory parasite. It must invade a host in order to carry out its life cycle.
Yes, there are many biologist who agree with your line of thinking. There are others who do not. Other biologist consider a virus to be a dormant code carrying cyst.
If the virus was truly dead, then it would not be able to carry out its mission.