Can medical laboratory tests detect if a woman is taking combined oral contraceptive pills?

"Combination" bcp's contain both estrogen and progestin, so while labs can detect both, the test would not "prove" a woman is actually taking bcp's, since both hormones are present (in smaller amounts) during the latter half of a regular menstrual cycle. If the lab test is done in the first half of the cycle, progesterone is not found if oral bcp's are being taken.

Generally not , since the routine blood tests are not going to be testing for the hormones in the pill, estrogen and progesterone . They do cause changes in the levels of different hormones , such as lowering the levels of oestradiol, DHEA , testosterone . and increasing the level of cortisol, but this is only seen in studies specifically looking for these hormones.