This paper presents SHARP (Supercomputing for High-speed Avoidance and Reactive Planning), a proof-of-concept study demonstrating how high-performance computing (HPC) can enable millisecond-scale responsiveness in robotic control. While modern robots face increasing demands for reactivity in human-robot shared workspaces, onboard processors are constrained by size, power, and cost. Offloading to HPC offers massive parallelism for trajectory planning, but its feasibility for real-time robotics remains uncertain due to network latency and jitter. We evaluate SHARP in a stress-test scenario where a 7-DOF manipulator must dodge high-speed foam projectiles. Using a hash-distributed multi-goal A* search implemented with MPI on both local and remote HPC clusters, the system achieves mean planning latencies of 22.9 ms (local) and 30.0 ms (remote, ~300 km away), with avoidance success rates of 84% and 88%, respectively. These results show that when round-trip latency remains within the tens-of-milliseconds regime, HPC-side computation is no longer the bottleneck, enabling avoidance well below human reaction times. The SHARP results motivate hybrid control architectures: low-level reflexes remain onboard for safety, while bursty, high-throughput planning tasks are offloaded to HPC for scalability. By reporting per-stage timing and success rates, this study provides a reproducible template for assessing real-time feasibility of HPC-driven robotics. Collectively, SHARP reframes HPC offloading as a viable pathway toward dependable, reactive robots in dynamic environments.