Would we know about a virus that causes no symptoms?
With the modern rise of meta-genomics, symptom-less viruses can be identified by the presence of their genomes. Certainly, there is more interest in pathogenic viruses than in harmless passengers, but today it's not necessary to have symptoms to identify viruses.  For example: 


  Investigators can now go beyond pathogenic viruses and have access to the thousands of viruses that inhabit our bodies without causing clinical symptoms. By studying their interactions with each other, with other microbes, and with host genetics and immune systems, we can learn how they affect health and disease. This article reviews current knowledge of the composition and diversity of the human virome in physiologically healthy individuals. It focuses on recent results from metagenomics studies and discusses the contribution of bacteriophages and eukaryotic viruses to human health.


--Metagenomics and the Human Virome in Asymptomatic Individuals.

Even prior to metagenomics, some "silent viruses" were identified: 


  Viruses are the most abundant obligate intracellular entities in our body. Until recently, they were only considered to be pathogens that caused a broad array of pathologies, ranging from mild disease to deaths in the most severe cases. However, recent advances in unbiased mass sequencing techniques as well as increasing epidemiological evidence have indicated that the human body is home to diverse viral species under non-pathological conditions.


--Describing the Silent Human Virome with an Emphasis on Giant Viruses