How long can someone survive with leukocytosis?

It depends on type. Leukocytosis (increased number of white blood cells) can be caused by infection, inflammation, allergic reaction, malignancy, hereditary disorders, or other causes. The subtype of white blood cells affected is alsoan important consideration. Survival depends on the reason for the leukocytosis and the treatment regimen followed.
A long time. Leukocytosis merely means that the white blood count is elevated above normal. It is usually caused by inflammation, often an infection, and should resolve as the inflammation clears. Life should not be shorted by such events. Obviously, there are malignant causes such as leukemia that can be life-threatening but that disease can often be cured as well.