The intensities and timescales of gradual solar energetic particle (SEP) events at 1 AU may depend not only on the characteristics of shocks driven by coronal mass ejections (CMEs), but also on large-scale coronal and interplanetary structures. It has long been suspected that the presence of coronal holes (CHs) near the CMEs or near the 1-AU magnetic footpoints may be an important factor in SEP events. We used a group of 41 E≈ 20 MeV SEP events with origins near the solar central meridian to search for such effects. First we investigated whether the presence of a CH directly between the sources of the CME and of the magnetic connection at 1 AU is an important factor. Then we searched for variations of the SEP events among different solar wind (SW) stream types: slow, fast, and transient. Finally, we considered the separations between CME sources and CH footpoint connections from 1 AU determined from four-day forecast maps based on Mount Wilson Observatory and the National Solar Observatory synoptic magnetic-field maps and the Wang–Sheeley–Arge model of SW propagation. The observed in-situ magnetic-field polarities and SW speeds at SEP event onsets tested the forecast accuracies employed to select the best SEP/CH connection events for that analysis. Within our limited sample and the three analytical treatments, we found no statistical evidence for an effect of CHs on SEP event peak intensities, onset times, or rise times. The only exception is a possible enhancement of SEP peak intensities in magnetic clouds.