The nonadiabatic alignment dynamics of weakly bound molecule-atom complexes, induced by a moderately intense 300 fs nonresonant laser pulse, is calculated by direct numerical solution of the time-dependent Schrödinger equation. Our method propagates the wave function according to the coupled channel equations for the complex, which can be done in a very efficient and stable manner out to large times. We present results for two van der Waal complexes, CS2-He and HCCH-He, as respective examples of linear molecules with large and small moments of inertia. Our main result is that at intensities typical of nonadiabatic alignment experiments, these complexes rapidly dissociate. In the case of the CS2-He complex, the ensuing rotational dynamics resembles that of isolated molecules, whereas for the HCCH-He complex, the detachment of the He atom severely perturbs and essentially quenches the subsequent rotational motion. At intensities of the laser pulse ≲2.0 × 1012 W/cm2, it is shown that the molecule-He complex can rotate and align without breaking apart. We discuss the implications of our findings for recent experiments on iodine molecules solvated in helium nanodroplets.