The dangly bits do affect induced drag. There is a relation between Lift and Induced drag.
Cdi = Cl^2/Pi*e*AR
Cdi = Coefficient of induced drag
Cl = Coefficient of lift
Pi = 3.14...
e = Oswald Efficiency Factor
AR = Aspect Ratio
By changing slats and flaps configurations, the coefficient of lift changes and so will the coefficient of induced drag.