...testosterone will definitely cause an increase in the percentage of red blood cells (erythrocytes ) in the blood. Too many red blood cells tend to thicken your blood, making it easier to clot, especially in smaller vessels. Very excessive red blood cells could actually be dangerous for your heart for this reason. But on the other hand, too little erythrocytes, results in anemia, tiredness, fatigue, etc.
White blood cells (or leukocytes), are what comes to the rescue when you get sick.
I'm not sure what the interaction between the two are. e.g. if you have too many red blood cells, does that mean you can't have as many white ones causing your infection fighting capabilities to be compromised. I seriously doubt that as I've never heard of people with high test levels being more prone to sickness.