Gravitational waves sap orbital angular momentum and energy from a black hole-neutron star (BH-NS) binary, driving it to inspiral and merge. In the violence of merger, the NS may tidally disrupt and form a hot accretion disk with the collimated magnetic fields necessary to launch jets, providing the central engine for one of the most energetic phenomena in the Universe: a gamma-ray burst (GRB). We assess the feasibility of this scenario with numerical relativity simulations of magnetized BH-NS binary mergers, seeding the NS with magnetic fields and exploring their effects on the remnant disk and the gravitational waves. We find that the gravitational waves are likely to be detectable by Advanced LIGO if the merger occurs within around 100Mpc, though the effects of magnetic fields on the waveforms are likely negligible. Further, we find that a GRB central engine may form if large-scale poloidal magnetic fields anchored in the disk are accreted onto the BH after the NS disrupts.