I don't think you should put it down. If it recovers, there are things you can do to help it live a normal life.
Here's what information I could find. I don't know what the likekihood of its survival is, but it's worth a try to save it. The link at the bottom is where I got the info.
"An animal in shock may show pale gums, cool extremities (including ears), glassy or closed eyes, weak pulse, increased rate of breathing and increased heart rate. If you feel that your rabbit may be in shock, wrap it in a towel, provide supplemental heat (if possible) and place the rabbit in a carrier for immediate transport to a vet clinic .... Injuries can occur that result in tearing of the skin. Bleeding will not usually be serious, unless the injuries are deeper than the skin. Lacerations to the skin can occur if two rabbits get into a fight, or if a rabbit is bitten by another animal. Bites are always considered very serious in rabbits and should be dealt with immediately upon discovery. If you see bleeding from a wound and it appears to be pulsing or gushing, this means that an artery may have been damaged. If the blood is seeping, this usually implies bleeding from veins. Using a sterile gauze pad (or if that is not readily available), a clean towel or cloth, apply firm, but gentle, pressure directly over the wound. If a pad becomes saturated with blood, do not remove it, but apply another one over it and continue applying pressure until you get to the veterinary clinic. Make sure you assess the gum color by lifting up the lip and looking at the tissue above the teeth. You can evaluate the capillary refill time by gently pushing on the gum tissue and watching to see how quickly the color returns to the tissue (in a normal rabbit, this should take less than 1.5 seconds).
If possible, bite wounds should be flushed with copious amounts of warm, soapy water (unless the wounds are deeper than the skin, in which case you should wait until you can seek professional care). Povidone iodine solution, diluted to iced tea color in warm water, is wonderful for flushing superficial wounds. In a pinch, antiseptic soap and warm water can be used to clean wounds. If you think that your rabbit may be in shock, do not waste precious time cleaning wounds at home. Flushing wounds may also exacerbate shock by further chilling the rabbit."
Thanks! It seems to be a bit better and no longer bleeding. My mom picked up some baby animal formula and it drank a bit. She also has in in a dark box with towels and a heat source.
Still waiting for the wildlife rehab to call back. Fingers crossed.