Not exactly. You could have symptoms but still not get tested because your symptoms are not severe enough. The people being tested are disproportionately those with severe symptoms.
I think we should make a distinction between those who have the virus but suffer few if any symptoms, and those whose symptoms are severe enough to be reported or require treatment. The first group I would say did not have the coronavoris in anything but name and can be ignored, while the second group actually has the disease we need to count and be worried about.