I assumed what you were really meaning, just wanted to cover the obvious of how the mount appeared in the photo, when you drop the rack down, it appears to be 18 to 24" wide, and if I remember correctly I believe that rack has a weight rating of 150 pounds. Now when you begin mounting at the rear of that rack (i.e. with a bike rack) your leverage point begins to extend even more than the 24" or so, and an average bike rack loaded with bikes will be 150-200 pounds extended at a distance (leverage), it may not be strong enough.
My suggestion would to find something like the Thule bigmouth, and mount across the back pack rack, at least then the weight will be distributed in the manner that it was designed.
Thule 599xtr Big Mouth Upright Bike Carrier