We study the effect of drag induced by the Galactic hot halo on the two neutral hydrogen (HI) cloud complexes associated with the Large and Small Magellanic Clouds: the Magellanic Stream (MS) and the Leading Arm (LA). In particular, we adopt the numerical models of previous studies and re-simulate the tidal formation of the MS and LA with the inclusion of a drag term. We find that the drag has three effects which, although model-dependent, may bring the tidal formation scenario into better agreement with observations: correcting the LA kinematics, reproducing the MS column density gradient, and enhancing the formation of MS bifurcation. We furthermore propose a two-stage mechanism by which the bifurcation forms. In general, the inclusion of drag has a variety of both positive and negative effects on the global properties of the MS and LA, including their on-sky positions, kinematics, radial distances, and column densities. We also provide an argument which suggests that ram-pressure stripping and tidal stripping are mutually exclusive candidates for the formation of the MS and LA.