Does drag increase with increasing bypass ratio in turbofan engines?
According to this 1975 NASA report on the effects of turbofan engine bypass ratio, the drag does increase for increasing bypass ratios. In the report, they use the following drag coefficient equation:
$$
C_{D,prop}=C_{D,nacelle}\cdot \frac{A_{nacelle}}{S} = \frac{D_{nacelle}}{\rho_\infty A_{nacelle}} \cdot \frac{A_{nacelle}}{S}
$$
As shown below, the nacelle drag coefficient initially increases for increasing bypass ratio.


Since $\frac{A_{nacelle}}{S}$ also increases with bypass ratio, the propulsion system drag will increase as well. So drag is closely related to the frontal area of the engine.



(images taken from report linked above)