The dust evolution equations are just the advection equation (v_d is the dust velocity and v_g is the gas velocity)

\frac{\partial \rho_d}{\partial t} = \nabla \cdot (\rho v_d)

with a momentum equation

v_d^* = v_d + \Delta t \frac{\partial v_d}{\partial t} = v_g - v_{drag}

which when cast as a acceleration term gives

\frac{\partial v_d}{\partial t} = \frac{v_g - v_d - v_{drag}}{\Delta t}

Now it's possible that v_{drag} \propto \Delta t - so that the underlying equations are independent of \Delta t, but the coupling term does not \frac{v_g-v_d}{\Delta t}