We present an analysis of the relationship between the orientation of magnetic fields and filaments that form in 3D magnetohydrodynamic simulations of cluster-forming, turbulent molecular cloud clumps. We examine simulated cloud clumps with size scales of L ~ 2-4 pc and densities of n ~ 400-1000 cm^-3 with Alfven Mach numbers near unity. We simulated two cloud clumps of different masses, one in virial equilibrium, the other strongly gravitationally bound, but with the same initial turbulent velocity field and similar mass-to-flux ratio. We apply various techniques to analyze the filamentary and magnetic structure of the resulting cloud, including the DisPerSE filament-finding algorithm in 3D. The largest structure that forms is a 1-2 parsec-long filament, with smaller connecting sub-filaments. We find that our simulated clouds, wherein magnetic forces and turbulence are comparable, coherent orientation of the magnetic field depends on the virial parameter. Subvirial clumps undergo strong gravitational collapse and magnetic field lines are dragged with the accretion flow. We see evidence of filament-aligned flow and accretion flow onto the filament in the subvirial cloud. Magnetic fields oriented more parallel in the subvirial cloud and more perpendicular in the denser, marginally bound cloud. Radiative feedback from a 16 Msun star forming in a cluster in one of our simulations ultimately results in the destruction of the main filament, the formation of an HII region, and the sweeping up of magnetic fields within an expanding shell at the edges of the HII region.