Sorry, but I have no knowledge of the size of the Elinchrom Quadra "A" heads. The opening at the back of the Rapid Box is relatively smallish. My Nikon SB910 Speedlight fits with a bit of room to spare vertically, but not much extra room horizontally. My Alien Bee head would be way too large. The Rapid Box puts out a very nice light indeed, especially with the reflector dish and diffuser. Using that as a main right over the camera and my 20" Rapid Box immediately below the camera in a 2:1 lighting ratio makes a location shot almost as good as one shot in the studio.
Thank you all for your import, I figured the Westcott Rapid Box was made solely for Speedlights, however, I have adapted equipment to work with my Quadra Heads, The Head itself is only 3.3 in x 3.1 inches ( X 6 inches when you include the "stem", I did adapt a Lumodi Beauty dish useing a Lastolite adapter and it works awesome. If your not sure what the Quadra Ranger is, please check it out here on Adorama. Great lighting, 400 watts system, extremly portable, albiet a bit expensive, but worth it to my aging muscle