I have done so, but the equipment, no matter the size, causes one to either do one or the other, hunt, or photograph. I have the same trouble when I carry broadheads for deer along with blunts for squirrels!
The big camera goes in a dedicated pack for protection. It is a padded LowePro backpack with compartments for lenses and camera body (with lens attached. I also have carried a Bogen tripod with a grip-action ball head along.
In the field, I take time from hunting to photograph. Just photograph. Then, when the air feels gamey, the camera is set aside or packed up and I hunt. The compact digital (with mini "tabletop" or strap-on tripod gets me more pics. I am usually disappointed with the outcome, but sometimes very pleased, and "iffy" pics are salvaged in the editing program through cropping or playing with effects.
I haven't gotten the DSLR of my dreams, and am holding out for the funds for its dedication. The combination of activity so far leads me to the decision on my part to either do one or the other, as both suffer in combination.
That leads me to the conclusion that I am just not good enough at either of them yet, but what a fine goal for one to apply oneself!
This is a crop. If I had had a DSLR and tripod, and the right lens, I would have maybe gotten this as a full size image. But without a camera, I would have only a memory (fading) of a vague hunt in the past years somewhere.
Killdeer