Chicken Hawk is a full-service stop with plenty of horse feed as well as drinks and snacks for riders. You're almost to Foresthill so best to vet, take a short break if really needed, and get moving down the trail.
If you really feel the need, crews can park and hike in the mile or so from the road to the check. If you have a small bag, you might be able to have someone else's crew bring it in. Just make sure you have it worked out how to get it back.
I helped volunteer for the last 1/2 of the riders coming through there last year and I don't remember many with personal crew stuff. We seemed to have any major needs covered with ride supplies, including bee sting kits and ice.
~ Crysta