Can they detect ovarian cancer through a blood test?

Backward. There is no screening test for ovca. However, if you have ovarian cancer, a ca-125 level may or may not be elevated. If it is, it may be one thing monitired for response. Getting ca-125, an expensive blood test of unproven value before knowing you have the cancer is inded backward, costly, non-specific and can led to unnecessary worry.
Poorly. Some (not most) ovarian cancers make ca125 which can be assayed in the blood. There are so many false-positives and false-negatives that most physicians believe that the test should not be used routinely to screen every woman.