Should I not drink a sports drink before the blood test to give false results?

You're fine. Sports drinks do very little for you beyond replacing the water and electrolytes you lose from exercising, and they won't cause any misleading results that might affect the management of your health.
No. Sports drinks are high in carbohydrates and would definitely mess up certain blood tests. If you are about to do a diabetes test for example this would invalidate your test results. I would check with your doctor to see what tests you are having done but play it safe and avoid the gatorade.