If Kaweah Gap goes, the rest of the trail is likely to be wide open. Despite its relatively low elevation of about 10,500, it has been known to clear very late compared with the rest of the trail, even after the Whitney switchers, which start 1500 feet higher. Back country ranger usually doesn't venture in till much later, and SEKI trail conditions reports
here tend to be very conservative and several days behind actual events.
High SIerra Topix had Kaweah open a couple of weeks ago, so I would be amazed if there were any problem on the HST when you are scheduled. Scarce water, maybe. Water up at Lodgepole (there is no water at Crescent Meadow TH) and at the major streams - Mehrten, Nine Mile, Buck Creek, - little ones are likely to be dry.