Superluminous supernovae (SLSNe) are massive star explosions too luminous to be powered by traditional energy sources, such as radioactive 56Ni. These transients may instead be powered by a central engine, such as a millisecond pulsar or magnetar, whose relativistic wind inflates a nebula of high energy particles and radiation behind the expanding ejecta. We present 3D Monte Carlo radiative transfer calculations which follow the production and thermalization of high energy radiation from the nebula into optical radiation and, conversely, determine the gamma-ray emission that escapes the ejecta without thermalizing. We track the evolution of photons and matter in a coupled two-zone ("wind/nebula" and "ejecta") model, accounting for the range of radiative processes. We identify a novel mechanism by which gamma-gamma pair creation in the upstream pulsar wind regulates the mean energy of particles entering the nebula over the first several years after the explosion, rendering our results on this timescale insensitive to the (uncertain) intrinsic wind pair multiplicity. To explain the observed late-time steepening of SLSNe optical light curves as being the result of gamma-ray leakage, the nebular magnetization must be very low, epsB <~ 1e-6-1e-4. For higher epsB, synchrotron emission quickly comes to dominate the thermalized nebula radiation, and being readily absorbed because of its lower photon energies, results in the SN optical light curve tracking the spin-down power even to late times >~ 1 yr, inconsistent with observations. For magnetars to remain viable contenders for powering SLSNe, we conclude that either magnetic dissipation in the wind/nebula is extremely efficient, or that the spin-down luminosity decays significantly faster than the canonical dipole rate ~1/t^2 in a way that coincidentally mimicks gamma-ray escape.