Can you hike the JMT southbound on a Kearsarge Pass trailhead permit from Onion Valley?

Yes, and it is one of the better-kept strategies in Sierra permit planning. A wilderness permit for the Kearsarge Pass trailhead out of Onion Valley puts you over the crest and onto the John Muir Trail near the Charlotte Lake junction, around JMT mile 157. From there, hiking south covers roughly the final 100 miles of the JMT to Mount Whitney, and Inyo National Forest permits are meaningfully easier to obtain than Yosemite's Donohue Pass eligible permits, where 45 daily slots produce single-digit odds.

What you get is arguably the best sustained stretch of the trail: the climb out of Vidette Meadow, Forester Pass at 13,153 feet, which is the highest point on the JMT proper, Bighorn Plateau, Guitar Lake at 11,500 feet, and the finish at 14,505 feet on Whitney's summit, followed by the descent to Whitney Portal. What you miss is everything north: Yosemite, Thousand Island Lake, Evolution Basin.

Be honest about the difficulty profile. Kearsarge is itself a high pass, you start high and stay high, and this section is the most remote on the trail. It suits hikers with prior experience above 10,000 feet. Kearsarge Pass carries the highest demand of the Inyo JMT feeder trailheads, so reserve early anyway. Nearby entries like Baxter, Sawmill, Taboose, and Shepherd Pass reach the same trail with lighter competition and rougher approaches.