Do allergies cause an elevated white blood count?

Possibly: The total WBC count may be increased but the differential of the count may be more telling. Often, the eosinophils, basophils, or mast cells (or combo of any) may be higher than normal.

Generally not: The most prevalent white blood cell, the neutrophil, accounts for 50-70% of the white blood cell count, and isn't affected by allergies. Eosinophils, however, can be increased in severe allergies, but only account for 3-5% of white blood cells. This is generally not enough to affect the overall white blood cell count.