If I took the Plan B emergency contraceptive pill and then took blood work the following day, will the active ingredient, levonorgestrel, show up in the blood work results?

It just depends on what type of blood work is ordered.  For example, if the blood work ordered is to get a white blood cell count and check for healthy liver and/or kidney function, then no, Levonorgestrel will not show up in the test results.  However, if the blood work ordered is to test your level of hormones (like in a blood test to check the function of the thyroid), then yes, that blood test will show an elevated level of hormones which will most likely cause your doctor to ask if you currently take birth control pills or perhaps, if you have taken "Plan B" within the past 48 hours.