Do I have to shoot my arrows with broadheads to test for accuracy after sighting-in with field points?

Yes.  You should always test-fire your broadheads for grouping accuracy after sighting-in with field points.  Even though you may have purchased broadheads that are the same weight as the field points that you used for sighting-in, the broadhead’s shape differs from that of the field point’s shape and can yield slightly different aerodynamic results.  You may need to make a slight windage or elevation adjustment to your scope to bring the arrow with a broadhead to your desired point of impact.