Yes being stressed out and having anxiety or the stress or both can cause a high white blood cell count which is normal when stressed or having anxiety.
When the stress and anxiety go away the white blood cell count should return to normal levels.
When your stressed or suffering from anxiety the stress and anxiety can decrease the body's lymphocytes which lead to the high white blood cell count.
Infections which lead to inflammation can also cause high white blood cell counts so if you're not stressed or suffering from anxiety you should see a doctor about the high white blood cell count to make sure it doesn't lead to something more serious.
Still stress is not good for your health as well because stress also raises your blood pressure which causes strokes, heart attacks, hear disease and even death.