The Linac Coherent Light Source II (LCLS-II) will be a hard X-ray Free Electron Laser whose linac can deliver a 1.2 MW CW electron beam with bunch rates up to 1 MHz. To efficiently generate such a high power beam, Super-Conducting Radio-Frequency (SCRF) cavities will be installed in the upstream portion of the existing 3 km Linac at the SLAC National Accelerator Laboratory. The 9-cell niobium cavities will be cooled at 2K inside 35 cryomodules, each containing a string of eight of those cavities followed by a quadrupole. The strong electromagnetic fields in the SCRF cavities will extract electrons from the cavity walls that may be accelerated. Most such dark current will be deposited locally, although some electrons may reach several neighboring cryomodules, gaining substantial energy before they hit a collimator or other aperture. The power deposited by the field emitted electrons and the associated showers may pose radiation and machine protection issues at the cryomodules and also in other areas of the accelerator. Simulation of these effects is therefore crucial for the design of the machine. The in-house code Track3P was used to simulate field emitted electrons from the LCLS-II cavities, and a sophisticated 3D model of the cryomodules including all cavities was written to transport radiation with the Fluka Monte Carlo code, which was linked to Track3P through custom-made routines. This setup was used to compute power deposition in components, prompt and residual radiation fields, and radioisotope inventories.