Low white blood cell counts are certainly not normal and can be caused by something serious such as cancer or lead to cancer or other serious health issues.
If you experience symptoms of a low white blood cell count always see your doctor to get blood tests and other tests done so that you can be sure it's nothing serious.
Symptoms of a low white blood cell count are heart palpitations, dizziness, fatigue and shortness of breath.
You may also experience things such as sputum, nasal drainage and Pus formation (at the site of an injury or incision.)
The side effects of a low white blood cell count are like I mentioned above but very common side effects are the fatigue and shortness of breath.
Always get tested by a doctor if you feel like you have a low white blood cell account.