Traditional direct imaging surveys of exoplanets are limited by their reliance on thermal emission, potentially biasing our understanding of exoplanet demographics at wide separations. Hot-start planets, with higher luminosities during formation, are favored over cold-start giants, which are fainter and harder to detect. Sub-Jovian-mass planets at wide separations also remain largely unexplored. Hα emission from accreting planets offers an alternative method to estimate occurrence rates regardless of thermal evolution and, with sufficient sensitivity, enables searches for lower-mass planets. We present results from a deep HST/WFC3-UVIS Hα imaging survey of over 200 members in the ~2 Myr-old IC 348 region. Using a deep learning-based image classification model to separate real sources from cosmic-ray-induced false positives, we identify one new brown dwarf companion candidate and provide upper limits on Hα luminosities, accretion luminosities, and mass accretion rates for non-detections. Ultimately this study provides the most precise demographic constraints on an otherwise hidden population of long-period accreting protoplanets.