You're not going to eliminate the stretch reflex that way. You're still supporting the weight with your legs which means you're still storing the energy. Granted, not as much as a free squat. You have to release the hip flexors and then all your weight will be on the box.
Squat to a chair like your lifting or whatever's handy right now. Then lift your knees. All your weight is now on the box and all the energy you built up on the descent has dissipated through the chair. Do this when you box squat, except you don't actually have to lift your knees. That's just to teach you how it feels.
I've seen Stan Efferding do this thing where he descends to a box and as soon as he touches it he explodes up. Just throwing that out there.