It's possible that low white blood cell counts can make you fatigued and tired but most commonly when you're tired and fatigued due to a low blood cell count it's due to a low red blood cell count.
Your red blood cells carry oxygen throughout your body and when the red blood cells are not high enough it can lead to your body not getting the required oxygen level which can lead to weakness, tiredness and fatigue.
When you have low white blood cells you can sometimes feel tired and weak but mostly a low white blood cell count can lead to infections.
Still if you think you have either a low white blood cell count or a low red blood cell count you should see a doctor and have a blood test done so they can find and treat the problem.
A blood test can show whether or not you have low red or white blood cell counts.