Seismic tomography has revealed two large low shear velocity provinces (LLSVPs) in the lowermost mantle beneath the central Pacific and Africa. The LLSVPs are further shown to be compositionally different from their surroundings. Among several hypotheses put forth in recent years to explain the cause of the LLSVPs, one postulates that they are thermochemical piles caused by accumulation of subducted oceanic crust at the core-mantle boundary (CMB). Mineral physics experiments indicate that oceanic crust becomes denser than the surrounding mantle at lower mantle pressures. In addition, seismic observations provide evidence of subducted slabs arriving at the CMB. However, a major question pertains to whether subducted oceanic crust can survive viscous stirring associated with mantle plumes and accumulate into piles with the same spatial scale as LLSVPs. We perform a set of high-resolution convection calculations to examine this hypothesis by investigating the interaction of thin oceanic crust (6 km) with mantle plumes. Our results show that as subducted oceanic crust is swept toward upwelling plume regions, the majority of it is viscously stirred into the surrounding mantle. Only a small amount of oceanic crust may accumulate at the base of plumes, but it is consistently entrained away into the plume at a rate equal to or greater than it is accumulated. We find that it is difficult for subducted oceanic crust to accumulate into large thermochemical piles at the CMB.