Well, maybe. You can actually see both high and low WBC counts with bacterial AND viral infections.
So why can the WBC count go below normal with a viral infection? First you have to try to determine WHY the WBC count is low. For example, a low white blood cell count can be the result of a prior infection - too many WBCs have been called into action and have been used up. This makes an individual more susceptible to outside infections like viruses. So when a blood test is performed, the WBC will be low, and the person will have a secondary viral infection going on.
However, there are viruses that can lower the number of a particular type of white blood cell. For example, with neutropenia, certain viruses (e.g. Hepatitis B virus) can decrease the production of neutrophils. So, you may see a below normal neutrophil count in a viral infection.
The cautionary tale is this - viral and bacterial infections can BOTH raise/lower WBC counts. Leukopenia can be seen in some viral infections (HIV) or severe bacterial infections. Leukocytosis can be seen in some viral infections (infectious mononucleosis) or bacterial infections.