Going for routine blood work would a swollen tendon (tennis elbow) cause my cbc and wbc /differential to be abnormal since there is inflamation?

No: There's lots of different kinds of inflammation. It takes systemic or very severe local disease to affect the CBC.

Not likely: For an elevation of your WBC to occur, a systemic reaction would have to be taking place, which is usually not the case with simple tennis elbow. The other possibility is that if you truly have a "swollen" elbow and an elevated WBC, it may be possible you have an infectious process in your elbow. Discuss with your doctor.